Kinetic energy, temperature and RMS speed — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The average translational kinetic energy per molecule of an ideal gas is

• A. $\frac32k_BT$
• B. $k_BT$
• C. $\frac12k_BT$
• D. $3k_BT$

Question 2 · difficulty L2 · understanding

For an ideal gas, average translational kinetic energy depends only on

• A. absolute temperature
• B. molecular mass only
• C. pressure only
• D. volume only

Question 3 · difficulty L2 · understanding

RMS speed of ideal-gas molecules is given by

• A. $v_{rms}=\sqrt{\frac{3RT}{M}}$
• B. $v_{rms}=\frac{3RT}{M}$
• C. $v_{rms}=\sqrt{\frac{M}{3RT}}$
• D. $v_{rms}=RTM$

Question 4 · difficulty L2 · understanding

At the same temperature, lighter gas molecules generally have

• A. higher RMS speed
• B. lower RMS speed
• C. the same RMS speed regardless of mass
• D. zero RMS speed

Question 5 · difficulty L3 · application

If the absolute temperature of an ideal gas is quadrupled, its RMS speed changes by a factor of

• A. 2
• B. 4
• C. 1/2
• D. 16

Question 6 · difficulty L3 · application

Two gases are at the same temperature. Gas P has molar mass four times that of gas Q. The ratio $v_{rms,P}/v_{rms,Q}$ is

• A. 1/2
• B. 2
• C. 1/4
• D. 4

Question 7 · difficulty L3 · application

At what temperature will an ideal gas have twice the RMS speed it has at 300 K?

• A. 1200 K
• B. 600 K
• C. 900 K
• D. 150 K

Question 8 · difficulty L3 · application

Hydrogen and oxygen are at the same temperature. Taking molar masses 2 and 32 g mol$^{-1}$, the ratio $v_{rms}(H_2)/v_{rms}(O_2)$ is

• A. 4
• B. 16
• C. 1/4
• D. 2

Question 9 · difficulty L4 · application

The average translational kinetic energy per mole of an ideal gas is

• A. $\frac32RT$
• B. $RT$
• C. $3RT$
• D. $\frac12RT$

Question 10 · difficulty L4 · application

Gas P at 400 K and molar mass 16 has the same RMS speed as gas Q at temperature T and molar mass 64. What is T?

• A. 1600 K
• B. 800 K
• C. 400 K
• D. 100 K