Heat And Thermodynamics

MCQs Part 3

Question 42: A body cools from 50°C to 40°C in 5 minutes. The surrounding temperature is 20°C. In what further time (in minutes) will it cool to 30° C?

  1. 5
  4. 10

Question 43: In the previous question, what will be its temperature 5 minutes after reaching 40°C?

  1. 35°C
  3. 32°C
  4. 30°C
Multiple Choice Questions with One or more than one options is correct

Question 44: A metal rod is shaped into a ring with a small gap. If this is hated,

  1. the length of the rod will increase
  2. the gap will decrease
  3. the gap will increase
  4. the diameter of the ring will increase in the same ratio as the length of the rod

Question 45: The average translational energy and the rms speed of the molecules in a sample of oxygen gas at 300 K are and 484 m/s respectively. Assuming ideal gas behaviour, the corresponding values at 600 K are nearly

  1. , 968 m/s
  2. , 684 m/s
  3. , 968 m/s
  4. , 684 m/s

Question 46: Let , and respectively denote the mean speed, the root-mean-square speed, and the most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m.

  1. No molecule can have speed greater than .
  2. No molecule can have speed less than .
  3. .
  4. The average kinetic energy of a molecule is .

Question 47: Two identical containers A and B have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gas in A is and that in B is . The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The changes in the pressure in A and B are found to be and 1.5 respectively.

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

Question 48: A gas undergoes a process in which its pressure p and volume V are related as = constant. The bulk modulus for the gas in this process is

  1. np

Question 49: n moles of a gas expands from volume to at constant temperature T. The work done by the gas is

  3. nRT ln
  4. nRT ln

Question 50: A gas with = goes from an initial state (, , ) to a final state (,, ) through an adiabatic process. The work done by the gas is

Question 51: A gas may expand either adiabatically or isothermally. A number of p-V curves are drawn for the two processes over different ranges of pressure and volume. It will be found that

  1. two adiabatic curves do not intersect
  2. two isothermal curves do not intersect
  3. an adiabatic curve and an isothermal curve may intersect
  4. the magnitude of the slope of an adiabatic curve is greater than the magnitude of the slope of an isothermal curve for the same values of pressure and volume

Question 52: A gas expands such that its initial and final temperatures are equal. Also, the process followed by the gas traces a straight line on the p-V diagram.

  1. The temperature of the gas remains constant throughout.
  2. The temperature of the gas first increases and then decreases.
  3. The temperature of the gas first decreases and then increases.
  4. The straight line has a negative slope.

Question 53: The following are the p-V diagrams for cyclic processes for a gas. In which of these processes is heat absorbed by the gas?

Question 54: Two gases have the same initial pressure, volume and temperature. They expand to the same final volume, one adiabatically and the other isothermally.

  1. The final temperature is greater for the isothermal process.
  2. The final pressure is greater for the isothermal process.
  3. The work done by the gas is greater for the isothermal process.
  4. All the above options are incorrect.

Question 55: In the previous question, if the two gases are compressed to the same final volume,

  1. the final temperature is greater for the adiabatic process
  2. the final pressure is greater for the adiabatic process
  3. the work done on the gas is greater for the adiabatic process
  4. all the above options are incorrect.

Question 56: In the cyclic process shown on the V-p diagram, the magnitude of the work done is

Question 57: In the previous question,

  1. work is done by the gas
  2. work is done on the gas
  3. heat is absorbed by the gas
  4. heat is given out by the gas

Question 58: A cyclic process is shown in the p-T diagram. Which of the curves show the same process on a V-T diagram?

Question 59: A cyclic process is shown on the p-T diagram. Which of the curves show the same process on a V-T diagram?

Question 60: A cyclic process is shown on the p-T diagram. which of the curves show the same process on a p-V diagram?

Solution:

42, 43. If a body cools from temperature to in time t, when the surrounding temperature is , by Newton's law of cooling,

= ,

where c = constant.

44. See the hint to Q. Nos. 1 and 2.

45. Average translational energy of a molecule = , and rms speed = .

46. = = = =

47. Let , be the initial pressures in A and B respectively. When the gases double their volumes at constant temperature, their pressures fall to and

for A, = or =

for B, = or =

= .

Also, = and = .

=

= or = .

48. = =

or =

Now, k = = .

53. In a cyclic process, heat is absorbed by a gas when the work done by it is positive, i.e., when work is done by the gas.

Work is done by the gas if the closed curve in a p-V diagram is clockwise, with p on the y-axis and V on the x-axis. if the axes for p and V are interchanged, work done is positive for an anticlockwise curve.

54.

55.

56. For a cyclic process plotted on the p-V diagram, the work done = area inside the closed curve. Treat the circle as an ellipse of semimajor axis and semiminor axis .

58, 59, 60.

Identify each of the processes AB, BC, CA, etc., in the given cyclic process. Then compare with the given curves.

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