JEE Main Physics Heat And Thermodynamics Previous Year Questions with Solutions
For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Heat And Thermodynamics Previous Year Questions with Solutions is given below.
Multiple Choice with ONE correct answer
1.A constant volume gas thermometer works on [1980]
a)the principle of Archimedes
b)Boyle’s law
c)Pascal’s law
d)Charle’s law
Ans.(d)
2.A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36° C The temperature difference across the layer A is [1980]
a) 6°C b) 12°C
c) 18°C d) 24°C
Ans.
3.An ideal monoatomic gas is taken round the cycle ABCDA as shown in the P-V diagram (see figure). The workdone during the cycle is [1983-1 mark]
a) PV
b)2 PV
c)PV/2
d)Zero
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4.From the following statements, concerning ideal gas at any given temperature T, select the correct one (s). [1995-2 marks]
a)The co-efficient of volume expansion at constant pressure is the same for all ideal gases
b)The average translational kinetic energy per molecule of oxygen gas is 3kT, k being Boltzmann constant
c)The mean-free path of molecules increases with increase in the pressure
d)In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different
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6.Two metallic sphere S1 and S2are made of the same material and have got identical surface finish. The mass of S1 is thrice that of S2. Both spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S2 is [1995-2 marks]
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7.The average translational kinetic energy and the root mean square speed of molecules in a sample of oxygen gas at 300 K are 6.21 x 10-21J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour) [1997-1 mark]
a)12.42 x10-21J,968 m/s
b)8.78 x 10-21 J,684 m/s
c)6.21 x 10-21 J,968 m/s
d)12.42 x 10-21J,684 m/s
Ans.
8.The intensity of radiation emitted by the Sun has its maximum value at a wavelength of 510 nm and that emitted by the North star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperatures of the Sun and the North Star is [1997-1 mark]
a) 1.46 b) 0.69 c) 1.21 d) 0.83
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9.The average translational kinetic energy of 02 (molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of N2 (molar mass 28) molecules in eV at the same temperature is [1997-1 mark]
a) 0.0015 b) 0.003 c) 048 d) 0.768
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10.A vessel contains 1 mole of 02 gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (relative molar mass 4) at a temperature 2 T has a pressure of [1997-1 mark]
a) P/8 b) P c) 2P d) 8P
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11.A spherical black body with a radius of 12 cm radiates 450 W power at 500 K . If the radius is halved and the temperature doubled, the power radiated in watt would be : [1997-1 mark]
a) 225 b) 450 c) 900 d) 1800
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12.One mole of a monoatomic gas is heated at a constant pressure of 1 atmosphere from OK to 100K. If the gas constant R=8.32 J/mol K, the change in internal energy of the gas is approximately [1998]
a) 2.3J b) 46J
c) 8.67×103J d) 1.25xl03J
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13.An ideal gas heat engine is operating between 227°C and 127°C . It absorbs 104J of heat at the higher, temperature. The amount of heat converted into work is [1998]
a) 2000J b) 4000J c) 8000J d) 5600J
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14.A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [1999-2 marks]
a) 4RT b) 15RT c) 9RT d) 11RT
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15.The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300K is [1999-2 marks]
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16.Two monoatomic ideal gases 1 and 2 of molecular masses M1 and M2 respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]
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17.A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L3and L2 are the lengths of the gas column before and after expansion respectively, then T1/T2 is given by [2000-2 marks]
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18.A block of ice at – 10°C is slowly heated and converted to steam at 100°C. Which of the following curves represents the phenomen on qualitatively?[2000-2 marks]
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20.Starting with the same gas expands from volume Vt to V2 in three different ways. The work done by the gas is if the process is purely isothermal, W2 if purely isobaric and W3 if purely adiabatic. Then [2000]
a) W2 > W1 > W3 b) W2 > W3 > W1
c) W1 > W2 > W3 d) W1 > W3 > W2
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21.The plots of intensity versus wavelength for three black bodies at temperature Tp T2 and T3 respectively are as shown. Their temperatures are[2000-2 marks]
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22.Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be [2001-2 marks]
a)45°C
b)60°C
c)30°C
d)20°C
Ans.
23.In a given process on an ideal gas, dW = 0 and dQ < 0. Then for the gas [2001]
a)the temperature will decrease.
b)the volume will increase
c)the pressure will remain constant
d)the temperature will increase
Ans.
24.P-V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to [2001-2 marks]
a)He and Oz
b)02 and He
c)He and Ar
d)02 and N2
Ans.
25.An ideal gas is taken through the cycle A -> B —> C —>A, as shown in the figure. If the net heat supplied to the gas in the cycle is 5J, the work done by the gas in the process C —> A is [2002-2 marks]
a)-5J
b)-10J
c)-15J
d)-20J
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26.Which of the following graphs correctly represents the variation of b = -(dV/dP)/V with P for an ideal gas at constant temperature? [2002-2 marks]
Ans.
27.An ideal black body at room temperature is thrown into a furnace. It is observed that [2002-2 marks]
a)initially it is the darkest body and at later times the brightest.
b)it is the darkest body at all times
c)it cannot be distinguished at all times.
d)initially it is the darkest body and at later times it cannot be distinguished.
Ans.(a) According to Kirchhoff’s law, good absorbers are good emitters and bad reflectors. While at lower temperature, a black-body absorbs all the incident radiations. It does not reflect any radiation incident upon it when it is thrown in the furnace. Initially it is therefore the darkest body.
At later times, the black body attains the temperature of the hot furnace and so it radiates all types of wavelengths with maximum energy. It becomes the brightest of all.Option (a) represents the answer.
28. The graph, shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivite and absorptive powers of the two bodies.
a)Ex > Ey and ax <ay
b)Ex < Ey and ax >ay
c)Ex > Ey and ax >ay
d)Ex <Eyand ax <ay
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30.The PT diagram for an ideal gas is shown in the figure, where AC is an adiabatic process. Find the corresponding PV diagram. [2003-2 marks]
Ans.(b) An inspection of the P-T graph reveals that
1)AC is an adiabatic process (given)
2)AB is an isothermal process a T constant
3)BC is an isobaric process at P constant.
i)In all the four options, BC is an isobaric process
ii)AB is an isothermal process.
.•.pv = constant
Graph between P and V is a rectangular hyperbola of the form xy = constant.
Graphs (b) and (d) satisfy this condition Options (a) and (c) are therefore incorrect.
iii)AC is an adiabatic process (given). In P-V diagram, slope of AC> slope of AB because slope of adiabatic curve > slope of isothermal curve.
This condition is certainly not satisfied in option (d) where AC is a straight line at constant V. Here AC is an isochoric process. It is not an adiabatic process (d) is incorrect. Hence the ultimate correct process is (b).
31. 2kg of ice at -20°C is mixed with 5 kg of water at 20°C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container.It is given that the specific heats of water and ice are 1 kcal/kg°C and 0.5 kcal/kg0C while the latent heat of fusion of ice is 80kcal/kg°C
a)7 kg b) 6 kg c) 4 kg d) 2 kg
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32.Three discs A, B, and C having radii 2 cm, 4 cm and 6 cm respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. The power emitted by them are QA, QB and Qc [2004-2 marks]
a)Qa will be maximum b) QB will be maximum c) Qc will be maximum d) QA = QB = Qc
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33.If liquefied oxygen at 1 atmospheric pressure is heated from 50 K to 300 K by supplying heat at constant rate, the graph of temperature vs time will be
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34.Two identical rods are connected between two One of, them is at 100°C containing water and another is 0°C containing ice. If rods are connected in parallel then the rate of melting of ice is q1g/sec. If they are connected in series then the rate is q2. The ratio q2/q1 is
a)2 b) 4 c) 1/2 d) 1/4
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35.An ideal-gas initially at P1, V, is expanded to P2, V2 and then compressed adiabatically to the same volume V1 and pressure P3. If W is the net work done by the gas in complete process which of the following is true? [2004]
a)W>0; P3 > P1 b) W<0; P3>P1
c) W>0; P3<P1 d) W<0;P3<P1
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36.Variation of radiant energy emitted by Sun, filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure.Which of the following option is the correct match ? [2005-2 marks]
a)Sun —T3 tungsten filament— T1, welding arc —T2
b)Sun-T2, tungsten filament— T1, welding arc—T3
c)Sun —T3, tungsten filament —T2, welding arc —T3
d)Sun —T1, tungsten filament—T2, welding arc— T1
Ans.
37.In which of the following processes, heat convection does not take place primarly? [2005-2 marks]
a)land and sea breeze b) boiling of water
c)heating air around a furance d)warming of glass of bulb due to filament.
Ans.(d)Warming of glass of bulb due to filament is due to radiation primarily. For convection process, a medium is required which can move between two points to transfer heat. Bulb is almost evacuated to have no medium. Option (d) represents the answer.
38.A spherical body of area A and emissivity e = 0.6 is kept inside a perfectly black body. Energy radiated per second by the body at temperature T
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39.Calorie is defined as the amount of heat required to raise temperature of 1 g of water by 1°C and it is defined under which of the following conditions ? [2005-2 marks]
a)From 14.5°C to 15.5°C at 760 mm of Hg
b)From 98.5°C to 99.5°C at 760 mm of H
c)From 13.5°C to 14.5°C at 76 mm of Hg
d)From 3.5°C to 4.5°C at 76 mm of Hg
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40.Water of volume 2 litre in a container is heated with a coil of power lkW at 27°C. The lid of the container is open and energy dissipates at rate of 160 J/s. In how much time temperature will rise from 27°C to 77°C. [Given specific heat of water is 4.2 kJ/kg]
a)7 min b) 6 min 2 s
c) 8 min 20 s d) 14 min
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41.An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is[2008]
a)l/T b) 2/T c) 3/T d) 4/T
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42.At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1930 m/s. The gas is [1984-2 marks]
a)H2 b) F2 c) 02 d) Cl2
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43.70 calorie of heat are required to raise the temperatureof 2 mole of an ideal gas at constant pressure from 30°C to 35°C.The amount of heat required (in calorie) to raise the temperature of the same gas through the same range (30°C to 35°C) at constant volume is [1985-2 marks]
a)30 b) 50 c) 70 d) 90
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44.Steam at 100°C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02kg at 15°C till the temperature of the calorimeter and its contents rises at 80°C.The mass of the steam condensed in kilogram is [1986-2 marks]
a)0.130 b)0.065 c)0.260 d)0.135
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45.Acylinder of radius R,made of a material of thermal conductivity K1, is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a materialof thermal conductivity K2.The two ends of the combined system are maintained at two different temperatures.There is no loss of heat across the cylindrical surface and the system is in steady state.The effective thermal conductivity of the system is [1988-2 marks]
a)K1 + K2 b)K1K2(K1 +K2)
c) (K1 +3K2)/4 d) (3K1 +K2)/4
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47.A real gas behaves like an ideal gas if its [2010]
a)pressure and temperature are both high
b)pressure and temperature are both low
c)pressure is high and temperature is low
d)pressure is low and temperature is high
Ans.(d) At low pressure and high temperature, the interaction between molcules approaces to zero. Therefore real gas is behaves as ideal gas.
48.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T: , the work done in the process is [2011]
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Multiple Choice with ONE or More Than ONE correct answers
49.For an ideal gas [1989-2 marks]
a) the change in internal energy in a constant pressure process from temperature T1 to T2 is equal to nCv (T2 -T1) , where Cv is the molar specific heat at constant volume and n the number of moles of the gas.
b) the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
c) the internal energy does not change in an isothermal process.
d) no heat is added or removed in an adiabatic process.
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50.When an ideal diatomic gas is heated at constant pressure ,the fraction of the heat energy supplied which increases the internal energy of the gas is
a)2/5 b)3/5 c)3/7 d)5/7
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51.Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities.Vessel A contains only 02,B only N2 and C a mixture of equal quantities of 02 and N2. If the average speed of the 02 molecules in vessel A is V1 that of the N2 molecules in vessel B is v2, the average speed of the 02 molecules in vessel C is Where M is the mass of an oxygen molecule [1992-2 marks]
Ans.(b) According to Maxwell’s distribution of speed of gas, the average speed of molecules
52. An ideal gas is taken from the state A (pressure P, volume V) to the state B(pressure P/2,volume 2V) along a straight line path in the P-V diagram. Select the correct statement (s) from the following. [1993-2 marks]
a)The workdone by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm.
b)In the T-V diagram, the path AB becomes a part of a parabola.
c)In the P-T diagram ,the path AB becomes a part of a hyperbola.
d)In going from A to B ,the temperature j of the gas first increases to a maximum value and then decreases.
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54.The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root -mean square velocity of the gas molecules is v, at 480 K it becomes [1996-2 marks]
a) 4v b) 2v c) v/2 d) v/4
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56.A given quantity of an ideal gas is at pressure P and absolute temperature T.The isothermal bulk modulus of the gas is [1998-2 marks]
a)2|3 p b) P c)3|2 p d)2P
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57.Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K.The piston of A is free to move,while that of B is held fixed.The same amount of heat is given to the gas in each cylinder.If the rise in temperature of the gas in A is 30K, rise in temperature of the gas in B is [1998-2 marks]
a) 30K b) 18 K c) 50 K d) 42 K
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58.During the melting of a slab of ice at 273 K at atmospheric pressure [1998-2 marks]
a)positive work is done by the ice-water system on the atmosphere
b)positive work is done on the ice-water system by the atmosphere
c)the internal energy of the ice-water system increases.
d)the internal energy of the ice-water system decreases.
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59.A black body is at a temperature of 2880 K. The ‘ energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien constant b = 2.88 x 106 nm K. Then [1998-2 marks]
a) U1 = 0 b) U3 = 0
c) U1 > U2 d) U2 > U1
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61.A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per 02 molecule to that per N2 molecule is [1998-2 marks]
a)1:1 b) 1:2
c) 2:1 d) depends on the moments of inertia of the two molecules
Ans.
62.A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The coefficients of linear expansion of the two metals are ac and aB. On heating, the temperature of the strip goes up by DT and the strip bends to form an arc of radius of curvature R. Then R is : [1999-3 marks]
a)proportional at DT
b)inversely proportional to DT
c)proportional to |aB – ac|
d)inversely proportional to |aB – ac|
Ans.
63.Initially a black body at absolute temperature T is kept inside a closed chamber at absolute temperature T0. Now the chamber is slightly opened to allow Sun rays to enter. It is observed that temperatures T and T0 remains constant. Which of the following statements is/are true? [2006-5 marks]
a)The rate of emission of energy from the black body remains the same
b)The rate of emission of energy from the black body increases
c)The rate of absorption of energy by the black bo-‘-y increases.
d)The energy radiated by the black body equals he energy absorbed by it.
Ans.(a,d) From Stefan’s law, the rate of emission of energy from a black body is proportional to (T-To )4 Since T and T0 remain constant, the rate of emission of energy remains the same. Since the temperature of the black body remains constant, the energy radiated by it = energy absorbed by it. Hence the correct choices are (a) and (d).
64.One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choice the correct option(s) from the following. [2010]
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65.Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then [2009]
a)Cp – Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas
b)Cp + Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas
c)Cp/Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas
d)Cp . Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas
Ans.
66.The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then, [2009]
a)the process during the path A B is isothermal
b)heat flows out of gas during the path B —>C—>D
c)work done during the path A—>B—>C is zero
d)positive work is done by the gas in the cycle ABCDA
A composite block is made of o il_____________ sl 6l
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67.slabs A, B, C, D and E of h“‘ different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat ‘Q’ flows only from left to right through the blocks. Then in steady state [2011]
a)heat flow through A and E slabs are same
b)heat flow through slab E is maximum
c)temperature difference across slab E is smallest
d)heat flow through C = heat flow through B + heat flow through D
Ans.
Assertion & Reasoning type
Instructions : The following question contains statement -1 (assertion) and statement -2 (reason) Of these statements, mark correct choice if
a)Statement – 1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement – 1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement – 1 is true, statement-2 is flase
d)Statement – 1 is false, statement-2 is true.
68.Statement-1: The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume. Statement-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision [2007-3 marks]
Ans.(b)
Matching Type
69.Heat given to process is positive, match the following option of column I with the corresponding option option of column II [2006-6 marks]
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70.Column I gives some devices and column II gives some processes on which the functioning of these devices depend. Match the device in column I with the processes in column II. [2007-6 marks]
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71.Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process.
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72.Column II gives certain systems undergoing a process. Column I sugests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process (es) from Column II. [2009]
Ans.p) When an uncharged capacitor is connected to a battery, it becomes charged and energy is stored in the capacitor.
q) When a gas in an adiabatic container fitted with an adiabatic piston is compressed by pushing the piston then internal energy of the system increases du = dQ – dW = O – ( Pdv) = + Pdv.
Mechanical energy provided to the system (by the moment of the piston) is converted into kE of gas molecules.
r) As the gas in a rigid container gets cooled, the internal energy of the system will decrease. The average KE per molecule will decrease. Hence None of the options in column I matches.
s) When a heavy nucleus initially at rest splits into two nuclei of nearly equal masses and some neutrons are emitted then (i) internal erergy of the system is converted into mechannical energy (ii) mass of the system decreases which converts into energy.
t) When a resistive wire loop is placed in a time varying magnetic field per pendicular to its plane, (i) Induced current shows in the loop due to which the energy of system is increased.
73.One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P.V.diagram. Column II given the characteristics involved in the cycle. Match them with each of the processes given in Column I
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76.A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same cross-section. At 25°C» the composite rod is 1 metre in length, of which the length of the copper rod is 30cm. At 125°C the length of the composite rod increases by 1.91mm.When the composite rod is not allowed to expand by holding it between two rigid walls, it is found that the length of the two constituents do not change with the rise of temperature. Find the Young’s modulus and the coefficient of linear expansion of the second rod.[Given : Coefficient of linear expansion of copper = 1.7xI0-5per°C, Young’s modulus of copper 1.3×1011N/m2 ]
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77.A solid material is supplied with heat at constant rate. The temperature of the material is changing with the heat input as shown in the graph in figure.Study the graph carefully and answer the following questions.
i)What do the horizontal region AB and CD represent ?
ii)If CD is equal to 2AB, what do you infer?
iii)What does the slope of DE represent?
iv)The slope of OA > the slope of BC. What does this indicate ? [1980]
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78.A jar contains a gas and a few drops of water at T K .The pressure in the jar is 830 mm of Hg. The temperature of the jar is reduced by 1%. The saturated vapour pressures of water at the two temperatures are 30 and 25mm of Hg. Calculate the new pressure in the jar. [1980]
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79.A lead bullet just melts when stopped by an obstacle. Assuming that 25% of the heat is absorbed by the obstacle, find the velocity of the bullet if its initial temperature is 27°C. (Meltging point of lead = 327°C. Specific heat of lead = 0.03 cal/g°C, Latent heat of fusion of lead = 6 cal/g, J = 4.2 J/cal.) [1981-3 marks]
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80.A cyclic process ABCA shown performed with a constant mass of an ideal gas. Show the same process on a P-V diagram (In the figure, CA is Tl 12 parallel to the V-axis and BC is parallel to the T-axis) [1981-4 marks]
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81.Calculate the work done when one mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are 105N/m2and 6 litre respectively. The final volume of the gas is 2 litre. Molar specific heat of the gas at constant volume is 3R/2. [1982-8 marks]
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82.A solid sphere of copper of radius R and a hollow sphere of the same material of inner radius r and outer radius R are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster? [1982-2 marks]
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83.One gram mole of oxygen at 27°C and one atmospheric pressure is enclosed in a vessel.
i)Assuming the molecules to be moving with vnns, find the number of collisions per second which the molecules make with one square metre area of the vessel wall.
ii)The vessel is next thermally insulated and moved with a’constant speed v0. It is then suddenly stopped. The process results in a rise of the temperature of the gas by 1°C. Calculate the speed v0. [1983-8 marks]
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Workdone is negative as the volume in right chamber decreases.
85.Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0°C and a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at 62°C. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.[1985-6 marks]
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86.An electric heater is used in a room of total wall area 137m2 to maintain a temperature of +20°C inside it, when the outside temperature is -10°C. The walls have three different layer materials. The innermost layer is of wood of thickness 2.5cm, the ‘ middle layer is of cement of thickness 0 cm and the outermost layer is of brick of thickness 25.0 cm. Find the power of the electric-heater. Assume that there is no heat loss through the floor to the ceiling. The thermal conductivities of wood, cement and brick are 0.125, 1.5 and 1.0 watt/m°C respectively. [1986-8 marks]
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89.An ideal mono atomic gas is confined in a cylinder by a spring-loaded piston of cross-section 8.0 x l0_3 m2 Initially the gas is at 300 K and occupies a Volume of 2.4 x 10_3 m3 and the spring is in its relaxed (un stretched, uncompressed) state, The gas is heated by a small electric heater until the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied (in joule) by the heater. The force constant of the spring is 800QN/m, atmospheric pressure is 1.0×10-5 Nm-2. The cylinder and the piston are thermally insulated. The piston is massless and there is no friction between the piston and cylinder. Neglect heat loss through lead wires of the heater. The heat capacity of the heater coil is negligible. Assume the spring to be mass less.
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90.An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2.
i)How many degrees of freedom do the gas molecules have?
ii)Obtain the work done by the gas during the expansion as a function of the initial pressure P and volume V. [1970-7 marks]
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91.Three moles of an ideal gas(Cp=7/2 R) at pressurePA and temperature TA are isothermally expanded to twice the initial volume. The gas is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure PA.[1991-4+4 marks]
a)Sketch P-V and P-T diagrams for the complete processb)
b)Calculate the net workdone by the gas, and the net heat supplied to the gas during the complete process.
92.Two moles of the helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal, calculate the following quantities in this process :
a)The net change in the heat energy
b)The net work done
c)The net change in internal energy [1992-8 marks]
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93.A cylindrical block of length 0.4m and area of cross section 0.04 m2 is placed coaxially on a thin metal disc of mass 0.4 kg and the same cross-section. The upper face of the cylinder is maintained at a constant temperature of 400K and the initial temperature of the disc is 300K. If the thermal conductivity of the material of the cylinder is 10 watt/mK and the specific heat of the material of the disc is 600J/kgK, how long will it take for the temperature of the disc to increase to 350K? Assume, for purpose of calculation, the thermal conductivity of the disc to be very high and the system to be thermally insulated except for the upper face of the cylinder. [1992-8 marks]
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94.One mole of a monoatomic ideal gas is taken through the cycle shown in figure.
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95.An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are Q1 = 5960 J , Q2 = -5585 J , Q3 =-2908 J and Q4 = 3645 J, respectively. The corresponding quantities of work involved are W1 = 2200 J, W2 = -825 J, W3 = -1100 J, and W4
i)Find the value of W4
ii)What is the efficiency of the cycle?
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96.A closed container of volume 0.02 m3 contains a mixture of neon and argon gases, at a temperature of 27° C & pressure of 1 x 105 Nnr2 . The total mass of the mixture is 28 g. If the molar masses of neon and argon are 20&40 g mol1 respectively , find the masses of the individual gases in the container, assuming them to be ideal. [Universal gas constant R = 8.314 J/mol K ] [JEE ’94, 6]
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97.A gaseous mixture enclosed in a vessel of volume V consists of one mole of a gas A with g( = Cp/Cv)=5/3 & another gas B with g =7/5 at a certain temperature T. The molar masses of the gases A & B are 4 & 32 respectively. The gases A &B do not react with each other and are assumed to be ideal. The gaseous mixture follows the equation; py19/13 = const, in adiabatic processes.[1995-10 marks]
a)Find the number of moles of the gas B in the gaseous mixture.
b)Compute the speed of sound in the gaseous mixture at T = 300 K.
c)If T is raised by 1 K from 300 K, find the percentage change in the speed of sound in the gaseous mixture.
d)The mixture is compressed adiabatically to 1/5 of its initial volume V . Find the change in its adiabatic compressibility in terms of the given quantities.
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98.At 27°C two moles of an ideal monoatomic gas occupy a volume V. The gas expands adiabatically to a volume 2V. Calculate i) the final temperature of the gas, ii) change in its internal energy, and iii)the work done by the gas during this process.[1996-5 marks]
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99.The temperature of 100 gm of water is to be raised from 24° C to 90° C by adding steam to it. Calculate the mass of the steam required for this purpose. [1996-2 marks]
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100.A thin rod of negligible mass and area of cross section 4 x l0_6 m2, suspended vertically from one end, has a length of 0.5 m at 100°C. The rod is cooled to 0°C, but prevented from contracting by attaching a mass at the lower end. Find i) this mass, and ii) the energy stored in the rod. Given for the rod, Young’s modulus =1011N/m2, coefficient of linear expansion = 10-5 K-5 and g = 10m/s2 [1997-5 marks]
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101.A double pane window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m2 and thickness 0.01 m separated by a 0.05m thick stagnant air space. In the steady state, the room glass interface and the glass outdoor interface are at constant temperatures of 27°C and 0°C respectively. Calculate the rate of heat flow through the window pane. Also find the temperatures of other interfaces. Given thermal conductivities of glass and air as 0.8 and 0.08 W m_1K_1 respectively. [1997-5 marks]
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102.A sample of 2kg of mono-atomic helium (assumed ideal) is taken through the process ABC and another sample of 2kg of the same gas is taken through the process ADC (see figure). Given molecular mass of helium = 4
i)What is the temperature of helium in each of the states A,B,C and D?
ii)Is there any way of telling afterwards which sample of helium went through the process ABC and which went through the process ADC? Write yes or no.
iii)How much is the heat involved in each process ABC and ADC? [1997-5 marks]
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104.The apparatus shown in the figure consists of four glass columns a connected by horizontal sections. The height of two central columns B & C are 49 cm each. The two outer columns A & D are open to the atmosphere. A & C are maintained at a temperature of 95° C while the columns B & D are maintained at 5° C. The height of the liquid in A & D measured from the base are 52.8 cm & 51 cm respectively. Determine the coefficient of thermal expansion of the liquid. [1997-5 marks]
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105.One mole of an ideal mono- ‘ atomic gas is taken round 3P0 the cyclic process ABCA as shown in figure. Calculate
a)the work done by the gas
b)the heat rejected by the gas in the path CA and the heat absorbed by the gas in the path AB;
c)the net heat absorbed by the gas in the path BC;
d)the maximum temperature attained by the gas during the cycle. [1998-8 marks]
Ans.Number of mole of ideal monoatomic gas =n=l mole
106.A solid body X of heat capacity C is kept in an atmosphere whose temperature is TA = 300 K. At time t = 0, the temperature of X is T0 = 400K. It cools according to Newton’s law of cooling. At time t1 its temperature is found to be 350 K. At this time t1, the body X is connected to a larger box Y at atmospheric temperature TA, through a conducting rod of length L, cross-sectional area A and thermal conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area A of the connecting rod is small compared to the surface area of X. Find the temperature of X at time t = 3t1 [1998-8 marks]
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107.Two moles of an ideal monatomic gas, initially at pressure P( and volume Vp undergoes an adiabatic compression until its volume is V2. Then the gas is given heat Q at constant volume V2.
a)Sketch the complete process on a P-V diagram
b)Find the total workdone by the gas, the total change in its internal energy and the final temperature of the gas. [Give your answer in terms P1,V1,V2, Q and R], [1999-10 marks]
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108.Two moles of an ideal mono- atomic gas taken through a cycle ABCA as shown in the P-T diagram. During the process AB, pressure and temperature of the gas vary such that PT = constant. If Tj = 300 K, calculate
a)the work done on the gas in the process AB and
b)the heat absorbed or released by the gas in each of the processes. Give answer in terms of the universal gas constant R. [2000-10 marks]
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109.An ice cube of mass 0.1 kg at 0°C is placed in an isolated container which is at 227°C. The specific heat S of the container varies with temperature T according to the empirical relation S = A + BT, where A = 100 cal/kg-K and B = 2 x 10-2 cal/kg- K2. If the final temperature of the container is 27°C, determine the mass of the container. (Latent heat of fusion of water = 8 x 104 cal/kg. Specific heat of water = 103 cal/kg-K) [2001-5 marks]
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110.A 5 m long cylindrical steel wire with radius 2 x l0_3m is suspended vertically from a rigid support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses. (For the steel wire: Young’s modulus =2.1 x lO11Pa; Density = 7860 kg/m3; Specific heat = 420 J / kg – K ). [2001-5 marks]
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112.A cubical box of side 1 meter contains helium gas (atomic weight 4) at a pressure of 100N/m2. During an observation time of 1 second, an atom travelling with the root mean square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. Take R = (25/3)J/mol -K and k = 1.38 x l0-23 J/K [2002-5 marks]
a)Evaluate the temperature of the gas.
b)Evaluate the average kinetic energy per atom.
c)Evaluate the total mass of helium gas in the box.
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113.An insulated container containing mono atomic gas of molar mass M is moving with a velocity v0. If the container is suddenly stopped, find the change in temperature.
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114.Hot oii is circulated through an insulated container with a wooden lid at the top whose conductivity K = 0.149 J/(m-°C-sec), thickness t = 5 mm, emissivity = 0.6. Temperature of the top of the lid is maintained at Tl = 127°. the ambient temperature Ta = 27°C. Calculate[2003-4 marks]
a)rate of heat loss per unit area due to radiation from the lid. .
b)temperature of the oil. (Given s = 17/3 x 10-8 Wm-2 K-4 )
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115.A diatomic gas is enclosed in a vessel fitted with mass less movable piston. Area of cross section of vessel is lm2. Initial height of the piston lm (see the figure). The initial temperature of the gas is 300 K. The temperature of the gas is increased to 400K, keeping pressure constant. Calculate the new height of the piston. The piston is brought to its initial position with no heat exchange. Calculate the final temperature of the gas. You can leave answer in fraction. [2004-2 marks]
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116.A small spherical body of radius r is falling under gravity in viscous medium. Due to friction, the medium gets heated. How does the rate of heating depend on radius of body when it attains terminal velocity?
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119.A cylinder of mass 1kg is given heat of 20,000J at atmospheric pressure.If initially the temperature of cylinder is 20°C, find
a)final temperature of the cylinde
b)workdone by the cylinder
c)change in internal energy of the cylinder. (Given that specific heat of cylinder = 400J kg-1 °CT-1, co-efficient of volume expansion = 9 x lO_5 0CT-1, Atmospheric pressure =105N/m2 and Density of cylinder = 9000 kg/m3)
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121.A piece of ice (heat capacity = 2100 J kg-1 °C_1 and latent heat = 3.36 x lO5 J kg-1) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of the heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
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122.A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. In the initial temperature of the gas is Ti( (in Kelvin) and the final temperature is a Ti, the value of a is
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123.Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?
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True /False Type
125.The root-mean square speeds of the molecules of different ideal gases, maintained at the same temperature are the same. [1981-2 marks]
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126.The volume V versus temperature T graphs for a certain amount of a’perfect gas at two pressure P1 and P2 are as shown in figure. It follows from the graphs that P1 is greater than P2. [1982-2 marks]
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127.Two different gases at the same temperature have equal root mean square velocities. [1982-2 marks]
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128.The curves A and B in the figure show P-V graphs for an isothermal and an adiabatic process for an ideal gas. The isothermal process is represented by the curve A. [1985-3 marks]
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129.At a given temperature, the specific heat of a gas at constant pressure is always greater than its specific heat at constant volume.
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130.The root mean square (rms) speed of oxygen molecules (02) at a certain temperature T (absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged. [1987-2 marks]
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131.Two spheres of the same material have radii lm and 4m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is greater than that by the second.[1988-2 marks]
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Fill in the blanks
132.One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is……………… [1984-2 marks]
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133.The variation of temperature of a material, as heat is given to it at a constant rate, is shown in the figure. The state of the material at the point P is…………. [1985-2 marks]
Ans.A to B represents a change which occurs at con¬stant temperature when heat is added to the sys¬tem.From O to A = Temperature increases at solid state. AB = It represents change of state from solid to liquid when heat is added.Since P lies on AB, the material is partly solid and partly liquid.
134.During an experiment, an ideal gas is found to obey an additional law VP2 constant, The gas is initially at a temperature T, and volume V. When it expands to a volume 2V, the temperature becomes……………….[1987-2 marks]
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135. 300 grain of water at 25°C is added to 100 gram of ice at 0°C. The final temperature of the mixture is……… °C. [11989-2 marks]
Ans.Ice at o°Cgains heat first to melt int0 water at
0°Cand then this water gains heat for rise of its temperature if heat energy is available.
Heat required by ice for melting =mL
136.The earth receives, at its surface, radiation from the sun at the rate of 1400Win 2 The dislance of the centre of tire sun from the surface of the earth is 1.5×1011m and radius of the sun is 7×108m. Treating the sun as a black body, it follows from the above data that its surface temperature is………K.[1989-2 marks]
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137.A solid copper sphere (density p and specific heats) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0 K. The time required for the temperature of the sphere to drop to 100 k is……….. [1991-2 marks]
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138.A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. If the temperature difference between the outer and inner surface of the shell is not to exceed T, the thickness of the shell should not be less than……. [1991-1 mark]
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139.A substance of mass M kg requires a power input of P watt to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t second. The latent heat of fusion of the substance is…………….[1992-1 mark]
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140.A container of volume 1 m3 is divided into two equal parts by a partition. One part has an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be ……………………..[1993-1 mark]
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142.Two metal cubes A & B of same size are j tour arranged as shown in figure.The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A & B are 300 W/m° C and 200 W/m° C, respectively. After steady state is reached the temperature T of the interface will be ……………….[1996-2 marks]
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143.A ring shaped tube contains two ideal gases with equal masses and molar masses M, = 32 and M2 = 28. The gases are separated by one fixed partition and another movable stopper S which can move freely without friction inside the ring. The angle a as shown in the figure is ………………… degree. [1997-2 marks]
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144.A gas thermometer is used as a standard thermometer for measurement of temperature, when the gas container of the thermometer is immersed in water at its triple point 273.16 K, the pressure in the gas thermometer reads 3.0 x l04 N/m2. When the gas container of the same thermometer is immersed in another system, the gas pressure reads 3.5xl04N/m2 The temperature of this system is therefore ………………..°C [1997-1 mark]
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145.Earth receives 1400 W/m2 of solar power . If all the solar energy falling on a lens of area 2 m2 is focused on to a block of ice of mass 280 grams, the time taken to melt the ice will be……………..minute.(Latent heat of fusion of ice ~ 3.3 x 105 J/kg) [1997-2 marks]
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