Sample 1Medium
Hydrogen (molar mass 2 g mol⁻¹) is at 300 K. At what temperature will oxygen molecules (molar mass 32 g mol⁻¹) have the same rms speed as the hydrogen molecules?
- A
1200 K
- B
4800 K
- C
300 K
- D
19200 K
Show the answer
The answer is B.v_rms = √(3RT/M), so equal speeds need T/M equal: T = 300 × 32/2 = 4800 K.
- A.
1200 K uses the square root of the mass ratio (4) instead of the ratio itself (16).
- C.
300 K ignores the dependence of rms speed on molar mass.
- D.
19200 K uses 64 instead of the mass ratio 16.
NCERT: Class 11 Physics, Chapter 12, Kinetic interpretation of temperature
Sample 2NEET level
Consider the following statements about an ideal gas. 1. The average kinetic energy of a molecule is (3/2)k_BT, independent of the nature of the gas. 2. At the same temperature, oxygen molecules have a higher rms speed than hydrogen molecules. 3. If the absolute temperature of the gas is made four times, the rms speed of its molecules doubles. 4. The pressure of the gas is two-thirds of its translational kinetic energy per unit volume. Which of the above statements are correct?
- A
1 and 3 only
- B
2, 3 and 4 only
- C
1, 2, 3 and 4
- D
1, 3 and 4 only
Show the answer
The answer is D.Average kinetic energy is (3/2)k_BT for any gas, and v_rms = √(3k_BT/m) doubles when T is made four times, while lighter hydrogen moves faster than oxygen at the same T, so statement 2 is false. From kinetic theory P = (1/3)nmv̄² = (2/3)E, where E is the translational kinetic energy per unit volume, so statement 4 is true.
- A.
Leaves out statement 4, which is true: P = (2/3)E per unit volume.
- B.
Includes statement 2 and leaves out statement 1: v_rms ∝ 1/√m, so hydrogen is faster.
- C.
Statement 2 is false: oxygen, being heavier, has the lower rms speed.
NCERT: Class 11 Physics, Chapter 12 (Kinetic Theory), Kinetic interpretation of temperature