Heat And Thermodynamics

MCQs Part 1

Question 1: Two holes of unequal diameter and are cut in a metal sheet. If the sheet is heated,

  1. both and will decrease
  2. both and will increase
  3. will increase, will decrease
  4. will decrease, will increase

Question 2: In the previous question, the distance between the holes will

  1. increase
  2. decrease
  3. remain constant
  4. may either increase or decrease depending on the positions of the holes on the sheet and on the ratio .

Question 3: A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be

  1. proportional to l
  2. inversely proportional to l
  3. independent of l
  4. independent of A

Question 4: Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The materials of the rods have Young modulii and , and coefficients of linear expansion and . The junction between the rods does not shift if the rods are cooled.

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

Question 5: Three rods of equal length are joined to form an equilateral triangle ABC. D is the midpoint of AB. The coefficient of linear expansion is for AB, and for AC and BC. If the distance DC remains constant for small changes in temperature,

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

Question 6: When the temperature of a body increases from t to , its moment of inertia increases from I to . The coefficient of linear expansion of the body is . The ratio is equal to

Question 7: A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column does not change with temperature. Let = coefficient of volume expansion of the liquid and = coefficient of linear expansion of the material of the tube.

  1. =
  2. =
  3. =
  4. = 0

Question 8: In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures, and . The liquid columns in the two arms have heights and respectively. The coefficient of volume expansion of the liquid is equal to

Question 9: A solid whose volume does not change with temperature floats in a liquid. For two different temperatures and of the liquid, fractions and of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

Question 10: A solid with coefficient of linear expansion just floats in a liquid whose coefficient of volume expansion is . If the system is heated, the solid will

  1. sink in all cases
  2. continue to float in all cases
  3. sink if
  4. sink if

Question 11: A gas at absolute temperature 300 K has pressure

= .

Boltzmann constant = k = J/K. The number of molecules per is of the order of

  1. 100

Question 12: The root-mean-square (rms) speed of oxygen molecules at a certain absolute temperature is v. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed would be

  1. v
  3. 2v

Question 13: The average translational kinetic energy of (molar mass 32) at a particular temperature is 0.048 eV. The average translational kinetic energy of (molar mass 28) molecules in eV at the same temperature is

  1. 0.0015
  2. 0.003
  3. 0.048
  4. 0.768

Question 14: A gas has volume V and pressure p. The total translational kinetic energy of all the molecules of the gas is

  1. only if the gas is monoatomic
  2. only if the gas is diatomic
  3. if the gas is diatomic
  4. in all cases

Question 15: A closed vessel is maintained at a constant temperature. It is first evacuated and then vapour is injected into it continuously. The pressure of the vapour in the vessel

  1. increases continuously
  2. first increases and then remains constant
  3. first increases and then decreases
  4. none of the above

Question 16: When an air bubble rises from the bottom to the surface of a lake, its radius becomes double. Find the depth of the lake, given that the atmospheric pressure is equal to the pressure due to a column of water 10 m high. Assume constant temperature and disregard surface tension.

  2. 30 m
  3. 40 m
  4. 70 m
  5. 80 m

Question 17: Two containers of equal volume contain the same gas at pressures and and absolute temperatures and respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T. The ratio p/T is equal to

Question 18: Two identical containers joined by a small pipe initially contain the same gas at pressure and absolute temperature . One container is now maintained at the same temperature while the other is heated to . The common pressure of the gasses will be

Question 19: In the previous question, let be the volume of each container. All other details remain the same. The number of moles of gas in the container at temperature will be

Question 20: A horizontal cylinder has two sections of unequal cross-sections, in which two pistons can move freely. The piston are joined by a string. Some gas is trapped between the pistons. If this gas is heated, the pistons will

  1. move to the left
  2. move to the right
  3. remain stationary
  4. either (a) or (b) depending on the initial pressure of the gas

Solutions:

1, 2. When a body is heated, the distance between any two points on it increase. The increase is in the same ratio for any set of two points.

Choose diametrically opposite points across each hole in Q. No. 1, and points on the edges of the holes in Q. No. 2, and apply the above principle.

3. Let = coefficient of thermal expansion, Y = Young modulus of the wire. If the wire were free to contract, its decrease in length would be , where t = decrease in temperature. To maintain constant length, becomes the effective elongation.

strain = = .

Let T = tension stress = .

Using Y = , T = .

4. Tension must be the same in both the rods for their junction to be in equilibrium. Using the result of Q. No. 3,

= .

5. = = .

Neglect terms.

6. I =

=

or = =

or = .

7. Let and be the areas of cross-section of the tube at temperatures 0 and t respectively,

l = length of the liquid column (constant)

and be the volumes of the liquid at temperatures 0 and t respectively.

= =

= =

= = =

or = .

8. Let , and be the densities of the liquid at temperatures 0, and respectively

To balance pressure, =

or = .

11. Pressure p = nKT, where n = number of molecules per unit volume

n = = = .

12. c =

Here, T becomes double and M becomes half.

17. For a closed system, the total mass of gas or the number of moles remains constant.

= , = , p (2V) =

18, 19. See the hint to Q. No. 17.

20. The pressure of the gas remains constant, and is equal to the atmospheric pressure (for equilibrium of the `gas plus pistons' system). If the temperature of the gas is increased, its volume must increase. For this, the piston must move to the right.

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