Kinetic Theory CBSE Questions & Answers

1

A house has well-insulated walls. It contains a volume of 100 \({{\rm{m}}^{\rm{3}}}\) of air at 300 K. If the energy required to lift an object of mass m through a height of 2.00 m equals the energy required to increase the temperature of this air by 1.00\(^\circ \)C., what is the value of m?

A
5.87 \( \times \) \({\rm{1}}{0^{\rm{3}}}\) kg
B
6.18 \( \times \) \({\rm{1}}{0^{\rm{3}}}\) kg
C
6.03 \( \times \) \({\rm{1}}{0^{\rm{3}}}\) kg
Correct
D
6.67 \( \times \) \({\rm{1}}{0^{\rm{3}}}\) kg

2

One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process, acquiring 500 J of energy by heat. It then undergoes an isobaric process, losing this same amount of energy by heat. Determine the new temperature of the gas

A
316 K
Correct
B
301 K
C
343 K
D
333 K

3

One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process, acquiring 500 J of energy by heat. It then undergoes an isobaric process, losing this same amount of energy by heat. Determine the work done on the gas.

A
333 J
B
231 J
C
200 J
Correct
D
123 J

4

One mole of an ideal diatomic gas with \({{\rm{C}}_{\rm{V}}}\) = 5R/2 occupies a volume \({{\rm{V}}_{\rm{I}}}\) at a pressure \({{\rm{P}}_{\rm{i}}}\). The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process, it is found that the rms speed of the gas molecules has doubled from its initial value. The amount of energy transferred to the gas by heat is

A
4 \({{\rm{P}}_{\rm{i}}}\) \({{\rm{V}}_{\rm{I}}}\)
B
9 \({{\rm{P}}_{\rm{i}}}\) \({{\rm{V}}_{\rm{I}}}\)
Correct
C
6 \({{\rm{P}}_{\rm{i}}}\) \({{\rm{V}}_{\rm{I}}}\)
D
5 \({{\rm{P}}_{\rm{i}}}\) \({{\rm{V}}_{\rm{I}}}\)

5

Two moles of an ideal gas (\(\gamma = 1.4\)) expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. What is the final pressure of the gas?

A
1.59 atm
B
1.19 atm
C
1.39 atm
Correct
D
1.09 atm

6

Two moles of an ideal gas (\(\gamma = 1.4\)) expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. What are the initial and final temperatures?

A
346 K, 243 K
B
386 K, 263 K
C
366 K, 253 K
Correct
D
406 K, 273 K

7

Two moles of an ideal gas (\(\gamma = 1.4\)) expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. Find Q, W, and \(\Delta {{\rm{E}}_{{\rm{int}}}}\).

A
1 J, 4.22 kJ, -4.22 kJ
B
10 J, 4.44 kJ, -4.44 kJ
C
100 J, 4.88 kJ, -4.88 kJ
D
0, 4.66 kJ, -4.66 kJ
Correct

8

Air in a thundercloud expands as it rises. If its initial temperature was 300 K, and if no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled?

A
237 K
B
247 K
C
257 K
D
227 K
Correct

9

Four liters of a diatomic ideal gas (\(\gamma = 1.4\)) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. Determine the volume of the gas at the end of the adiabatic expansion.

A
8.55 liters
B
8.79 liters
Correct
C
8.97 liters
D
8.23 liters

10

Four liters of a diatomic ideal gas (\(\gamma = 1.4\)) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. Find the temperature of the gas at the start of the adiabatic expansion

A
789 K
B
865 K
C
984 K
D
900 K
Correct

11

Four liters of a diatomic ideal gas (\(\gamma = 1.4\)) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. Find the temperature at the end of the cycle

A
332 K
B
285 K
C
300 K
Correct
D
276 K

12

Four liters of a diatomic ideal gas (\(\gamma = 1.4\)) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. What was the net work done for this cycle?

A
336 J
Correct
B
376 J
C
316 J
D
356 J

13

Consider 2.00 mol of an ideal diatomic gas. Find the total heat capacity at constant volume and at constant pressure, if the molecules rotate but do not vibrate

A
9.85 cal/K, 13.7 cal/K
B
9.95 cal/K, 13.9 cal/K
Correct
C
9.65 cal/K, 13.5 cal/K
D
9.45 cal/K, 13.2 cal/K

14

According to Atomic Hypothesis:

A
little particles of atom attract each other when they are at small distance apart, but repel upon being squeezed into one another
Correct
B
little particles of atom repel each other when they are at large distance apart, but attract upon being separated from one another
C
little particles of atom repel each other when they are at small distance apart, but attract upon being squeezed into one another
D
little particles of atom repel each other when they are at small distance apart, but repel upon being squeezed into one another

15

The perfect gas equation can be written as

A
PV = \({{\rm{k}}_{\rm{B}}}\) N
B
PV = \({{\rm{k}}_{\rm{B}}}\) T
C
PV = \({{\rm{k}}_{\rm{B}}}\) NT
Correct
D
P = \({{\rm{k}}_{\rm{B}}}\) NT