Heat And Thermodynamics

MCQs Part 4

Question 61: The first law of thermodynamics incorporates the concepts of

  1. conservation of energy
  2. conservation of heat
  3. conservation of work
  4. equivalence of heat and work

Question 62: The internal energy of a system remains constant when it undergoes

  1. a cyclic process
  2. an isothermal process
  3. an adiabatic process
  4. any process in which the heat given out by the system is equal to the work done on the system

Question 63: For an ideal gas,

  1. the change in internal energy in a constant-pressure process from temperature to is equal to , where is the molar heat capacity at constant volume and n is the number of moles of the gas
  2. the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process
  3. the internal energy does not change in an, isothermal process
  4. no heat is added or removed in an adiabatic process

Question 64: The molar heat capacity for an ideal gas

  1. cannot be negative
  2. must be equal to either or
  3. must lie in the range
  4. may have any value between and

Question 65: The molar heat capacity for an ideal gas

  1. is zero an adiabatic process
  2. is infinite for an isothermal process
  3. depends only on the nature of the gas for a process in which either volume or pressure is constant
  4. is equal to the product of the molecular weight and specific heat capacity for any process

Question 66: is always greater than for a gas. Which of the following statements provide, party or wholly, the reason for this?

  1. No work is done by a gas at constant volume.
  2. When a gas absorbs heat at constant pressure, its volume must change.
  3. For the same change in temperature, the internal energy of a gas changes by a smaller amount at constant volume than at constant pressure.
  4. The internal energy of an ideal gas is a function only of its temperature.

Question 67: A system undergoes a cyclic process in which it absorbs heat and gives out heat. The efficiency of the process is and the work done is W.

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

Question 68: Heat is supplied to a certain homogenous sample of matter, at a uniform rate. Its temperature is plotted against time, as shown. Which of the following conclusions can be drawn?

  1. Its specific heat capacity is greater in the solid state than in the liquid state.
  2. Its specific heat capacity is greater in the liquid state than in the solid state.
  3. Its latent heat of vaporization is greater than its latent heat of fusion.
  4. Its latent heat of vaporization is greater than its latent heat of fusion.

Question 69: The two ends of a uniform rod of thermal conductivity k are maintained at different but constant temperatures. The temperature gradient at any point on the rod is (equal to the difference in temperature per unit length). The heat flow per unit time per unit cross-section of the rod is I.

  1. is the same for all points on the rod.
  2. I will decrease as we move from higher to lower temperature.
  3. I =
  4. All the above options are incorrect.

Question 70: Three rods of the same dimensions have thermal conductivities 3k, 2k and k. They are arranged as shown, with their ends at 100°C, 50°C and 0°C. The temperature of their junction is

  1. 75°C
  3. 40°C

Question 71: Five rods of the same dimensions are arranged as shown.They have thermal conductivities , , , and . When points A and B are maintained at different temperatures, no heat flows through the central rod. It follows that

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

Question 72: Three rods A, B and C have the same dimensions. Their thermal conductivities are , and respectively. A and B are placed end to end, with their free ends kept at a certain temperature difference. C is placed separately, with its ends kept at the same temperature difference. The two arrangements conduct heat at the same rate. must be equal to

Question 73: The three rods described in the previous question are placed individually, with their ends kept at the same temperature difference. The rate of heat flow through C is equal to the rate of combined heat flow through A and B. must be equal to

Question 74: One end of a uniform rod of length 1 m is placed in boiling water while its other end is placed in melting ice. A point P on the rod is maintained at a constant temperature of 800°C. The mass of steam produced per second is equal to the mass of ice melted per second. If specific latent heat of steam is 7 times the specific latent heat of ice, the distance of P from the steam chamber must be

Question 75: A and B are two points on a uniform metal ring whose centre is C. The angle ACB = . A and B are maintained at two different constant temperatures. When = 180°, the rate of total heat flow from A to B is 1.2W. When = 90°, this rate will be

  1. 0.6 W
  2. 0.9 W
  3. 1.6 W
  4. 1.8 W

Question 76: In a 10-metre-deep lake, the bottom is at a constant temperature of 4°C. The air temperature is constant at _ 4°C. The thermal conductivity of ice is 3 times that of water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be

  1. 7.5 m
  2. 6 m
  3. 5 m
  4. 2.5 m

Question 77: 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

Question 78: A spherical black body of radius r radiates power P, and its rate of cooling is R.

Question 79: The temperature of an isolated black body falls from to in time t. Let c be a constant.

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

Question 80: A planet is at an average distance d from the sun, and its average surface temperature is T. Assume that the planet receives energy only from the sun, and loses energy through radiation from its surface. Neglect atmospheric effects. It , the value of n is

  1. 2
  2. 1

Question 81: The solar constant for the earth is . The surface temperature of the sun is T K. The sun subtends an angle at the earth.

Question 82: The power radiated by a black body is P, and it radiates maximum energy around the wavelength . If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength , the power radiated by it will increase by a factor of

  1. 4/3
  2. 16/9
  3. 64/27
  4. 256/81

Question 83: Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of the two bodies are the same. The two bodies radiate energy at the same rate. The wavelength , corresponding to the maximum spectral radiancy in the radiation from B, is shifted from the wavelength corresponding to the maximum spectral radiancy in the radiation from A by 1.00 . If the temperature of A is 5802 K,

  1. the temperature of B is 1934 K
  2. =
  3. the temperature of B is 11604 K
  4. the temperature of B is 2901 K

Question 84: 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 , between 999 nm and 1000 nm is and between 1499 nm and 1500 nm is . The Wien constant is b = nm K.

  1. = 0
  2. = 0

Question 85: A body with an initial temperature is allowed to cool in a surrounding which is at a constant temperature of . Assume that Newton's law of cooling is obeyed. Let k = constant. The temperature of the body after time t is best expressed by

  2. ln (kt)

Question 86: A system S receives heat continuously from an electrical heater of power 10 W. The temperature of S becomes constant at 50°C when the surrounding temperature is 20°C. After the heater is switched off, S cools from 35.1°C to 34.9°C in 1 minute. The heat capacity of S is

  1. 100 J/°C
  2. 300 J/°C
  3. 750 J/°C
  4. 1500 J/°C

Question 87: A body cools in a surrounding which is at a constant temperature of . Assume that if obeys Newton's law of cooling. Its temperature is plotted against time t. Tangents are drawn to the curve at the point P ( = ) and Q ( = ). These tangents meet the time axis at angles of and , as shown

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

Solution:

64, 65. The molar heat capacity has the general definition

C = ,

where n = number of moles, = heat absorbed by the gas and = rise in temperature of gas.

It is possible to obtain almost any set of values for and by proper selection of a process.

68. The horizontal parts of the curve, where the system absorbs heat at constant temperature, must depict changes of state. Here the latent heats are proportional to the lengths heat capacity is inversely proportional to the slopes.

70. See the hint to Q. No. 38. Let = temperature of junction.

= = = .

Use Kirchhoff's first law to distribute current at the junction.

= , = , =

71. This is analogous to a balanced Wheatstone bridge.

= , etc., and = for balance.

72, 73. Use electrical analogues of resistances in series and parallel to find the termal resistances.

74.

Let and amounts of heat flow from P in any time t. Let m be the masses of steam formed and ice melted in time t. Let k and A be the thermal conductivity and the area of cross-section respectively of the rod.

= =

= =

Dividing, = 7

or 1 - x = 8x or x = .

75. Let R = total thermal resistance of the ring,

= difference in temperature between A and B.

For = 180°, two sections of resistance R/2 each are in parallel.

Equivalent resistance = R/4.

Rate of total heat flow = = 1.2 = .

or 0.3 =

For = 90°, two sections of resistance R/4 and 3R/4 are in parallel.

Equivalent resistance = = .

Rate of total heat flow

= = = = 1.6 W.

76. The rate of heat flow is the same through water and ice in the steady state.

I = =

x =

or x= 7.5 m.

77. Area of spherical shell = .

Rate of heat flow = P = , where d = thickness of shell.

78, 79. P = = =

Here, R = .

and .

= (constant)

or = t.

80. Let P = power radiated by the sun, R = radius of planet.

Energy received by planet = .

Energy radiated by planet = .

For thermal equilibrium, = .

or

or or .

81. Let R = radius of the sun, d = distance of the earth from the sun.

Power radiated by the sun = = P.

Energy received per unit area second normally on the earth

= = = =

=

Angle subtended by the sun at the earth = = .

or = .

82. Let = initial temperature of the black body.

= b (constant)

Power radiated = = (c = constant)

Let T = new temperature of black body.

= b =

or T = .

Power radiated = = = .

83. Let P and A be the power radiated and the surface area of both bodies respectively.

Let and be the absolute temperatures of A and B respectively.

P = =

or = or = = = 1934 K.

Also, =

or = or = .

Given, = 1 or = 1

or = = = 1.5 .

84. = b = nm K or = = 1000 nm.

The black body radiates maximum energy around .

is greater than or .

Also, energy is radiated at all wavelengths.

,

85. = , where k = constant.

= _

or = - kt

or [ln -ln = - kt

or =

or = .

86. Rate of loss of heat difference in temperature with the surroundings.

At 50°C, = k (50 _ 20) = 10, where k = constant

k =

At an average temperature of 35°C, = = 5 J/s.

Heat lost in 1 minute = = = 300 J = Q.

Fall in temperature = 0.2°C = .

Q = .

Heat capacity = c = = = 1500 J/°C.

87. For plot, rate of cooling = = slope of the curve.

At P, = = = ,

= .

Copyright © excellup 2014