Heat And Thermodynamics

MCQs Part 2

Question 21: A gas expands from 1 litre to 3 litres at atmospheric pressure. The work done by the gas is about

1. 2 J
2. 200 J
3. 300 J
4. 

Question 22: During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio = for the gas is

1. 2
2. 
3. 
4. 

Question 23: In the previous question, the gas may be

1. monoatomic
2. diatomic
3. a mixture of monoatomic and diatomic gases
4. a mixture of diatomic and triatomic gases

Question 24: Each molecule of a gas has f degrees of freedom. The ratio = for the gas is

1. 
2. 
3. 
4. 

Question 25: A mixture of moles of monoatomic gas and moles of diatomic gas has = = 1.5.

= = = =

Question 26: The pressure p of a gas is plotted against its absolute temperature T for two different constant volumes and , where . p is plotted on the y-axis and T on the x-axis.

1. The curve for has greater slope than the curve for .
2. The curve for has greater slope than the curve for .
3. The curves must intersect at some point other than T = 0.
4. The curves have the same slope and do not intersect.

Question 27: A cyclic process ABCD is shown in the p-V diagram. Which of the following curves represent the same process?

1. 
2. 
3. 
4. 

Question 28: The ratio = for a gas. Its molecular weight is M. Its specific heat capacity at constant pressure is

1. 
2. 
3. 
4. 

Question 29: The molar heat capacity of a gas at constant volume is . If n moles of the gas undergo change in temperature, its internal energy will change by

1. only if the change of temperature occurs at constant volume
2. only if the change of temperature occurs at constant pressure
3. in any process which is not adiabatic
4. in any process

Question 30: 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

1. 
2. 
3. 
4. 

Question 31: The average degree of freedom per molecule for a gas is 6. The gas performs 25 J of work when it expands at constant pressure. The heat absorbed by the gas is

1. 75 J
2. 100 J
3. 150 J
4. 125 J

Question 32: 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 30 K then the rise in temperature of the gas in B is

1. 30 K
2. 18 K
3. 50 K
4. 42 K

Question 33: A system is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system along these two paths are and and and respectively.

1. =
2. =
3. =
4. =

Question 34: Equal masses of three liquids A, B and C have temperatures 10°C, 25°C and 40°C respectively. If A and B are mixed, the mixture has a temperature of 15°C.If B and C are mixed, the mixture has a temperature of 30°C. If A and C are mixed, the mixture will have a temperature of

1. 16°C
2. 20°C
3. 25°C
4. 29°C

Question 35: If water at 0°C, kept in a container with an open top, is placed in a large evacuated chamber,

1. all the water will vaporize
2. all the water will freeze
3. part of the water will vaporize and the rest will freeze
4. ice, water and water vapour will be formed and reach equilibrium at the triple point

Question 36: In the previous question, if the specific latent heat of vaporization of water at 0°C is times the specific latent heat of freezing of water at 0°C,the friction of water that will ultimately freeze is

1. 
2. 
3. 
4. 

Question 37: A substance of mass M kg requires a power input of P watts to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t seconds. The specific latent heat of fusion of the substance is

1. Pt
2. 
3. PtM
4. 

Question 38: Two identical rods are made of different materials whose thermal conductivities are and . They are placed end to end between two heat reservoirs at temperatures and . The temperature of the junction of the rods is

1. 
2. 
3. 
4. 

Question 39: A cylinder of radius R, made of a material of thermal conductivity, is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The shell is made of a material of thermal conductivity . 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 conductivity of the system is

1. 
2. 
3. 
4. 

Question 40: A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watts would be

1. 225
2. 450
3. 900
4. 1800

Question 41: Two spherical black bodies of radii and and with surface temperatures and respectively radiate the same power. must be equal to

1. 
2. 
3. 
4. 

Solutions

21. At constant pressure, work =

22. = constant

or

Here,

or = 3 or = .

25. The average number of degrees of freedom per molecule,

f =

=

where = Avogadro constant.

Here, = 3, = 5

f = =

Also, = = 1.5 or f = 4

= 4.

26. pV = nRT or p =

For a p-T graph, slope = .

27. AB constant p, increasing V; increasing T

BC constant T, increasing V, decreasing p

CD constant V, decreasing p; decreasing T

DA constant T, decreasing V, increasing p

Also, BC is at a higher temperature than AD.

28. Specific heat capacity = .

30. = at constant pressure

=

Fraction = = = = for diatomic gas.

31. = =

= =

= = = .

= = 100 J.

32. = =

= = for diatomic gas

= = 42 K.

34. When systems of masses , , ..., specific heat capacities , , ... and initial temperatures , , ... are mixed, the temperature of the mixture is

= =

For systems of equal mass, = .

Let , and be the specific heat capacities of A, B and C respectively.

For A + B, 15 = or = or = .

For B + C, 30 = or = or = .

For A + C, = = = = 16.

35. Let = specific latent heat of vaporization,

= specific latent heat of freezing.

Given, = .

Let m = initial mass of water, f = fraction of water frozen.

Mass of vapour formed = m (1 _ f), mass of ice formed = .

=

or = =

or = f

or f = .

37. For thermal equilibrium in the molten state, the rate of absorbing heat = P = the rate of losing heat due to radiation, etc.

When the power source is turned off, the system continues to lose heat at the same rate, as its temperature does not change.

Therefore, heat lost in time t = Pt = required heat loss for complete solidification = ML, where L = specific latent heat of fusion.

38. Problems like this are best solved by using their electrical analogues.

For a rod length l, area of cross-section A and thermal conductivity k, we define the thermal resistance as

R = .

The given situation is like two resistances in series. We define the heat current I = .

As the resistances are in series, they carry the same current. Let be the temperature of their junction.

I = = , where = and =

or = = .

Solve for .

39.

See the hint to Q. No. 38. For the inner and outer cylinders, thermal resistances are

= and =

For an equivalent conductor of length l, radius 2R and thermal conductivity k, thermal resistance = =

, as the inner and outer cylinder are effectively in parallel between the same temperature difference.

40, 41. For spherical black body of radius r and absolute temperature T, the power radiated = .

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