Question

The average translational energy and the r.m.s. speed of molecules in a sample of oxygen gas at 300 K are $6.21 \times 10^{- 21}J$ and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

• A. (a) $12.42 \times 10^{21}J,\mspace{6mu} 968m/s$
• B. $8.78 \times 10^{21}J,\mspace{6mu} 684m/s$
• C. $6.21 \times 10^{21}J,968m/s$
• D. $12.42 \times 10^{21}J,\mspace{6mu} 684m/s$

Answer 1

Answer: (D)

$12.42 \times 10^{21}J,\mspace{6mu} 684m/s$

Answer 2

We know that average translational $K.E.$ of a molecule $= \frac{3}{2}kT$ At$300K,$ average $K.E. = 6.21 \times 10^{- 21}J$

At$600K,$ average $K.E = 2 \times (6.21 \times 10^{- 21})$

$= 12.42 \times 10^{- 21}J$

We know that $v_{rms} = \sqrt{\frac{3kT}{m}}$At $v_{rms} = 484m/s$

At $v_{rms}^{'} = \sqrt{2} \times 484 = 684m/s$