Q: The average translatory energy and r.m.s. speed of molecules in a sample of oxygen gas at 300 K are 6.21 × 10^{-21} J and 484 ms ^{-1} respectively. The corresponding values at 600 K are nearly: (assuming ideal gas behavior)

(a) 12.42 × 10^{-21} J , 968 ms^{-1}

(b) 8.78 × 10^{-21} J, 684 ms^{-1}

(c) 6.21 × 10^{-21} J, 968 ms^{-1}

(d) 12.42 × 10^{-21} J, 684 ms^{-1}

Ans: (d)

Sol: $ \displaystyle \frac{C_2}{C_1} = \sqrt{\frac{T_2}{T_1}}$

$ \displaystyle C_2 = C_1\sqrt{\frac{T_2}{T_1}}$

$\displaystyle C_2 = C\sqrt{\frac{2T}{T}} = C\sqrt{2}$

$\displaystyle C_2 = 484\sqrt{2}$

C_{2} = 684 m/s

$\displaystyle \frac{E_2}{E_1} = \frac{C_2^2}{C_1^2} = \frac{(C\sqrt{2})^2}{C^2}$

$\displaystyle \frac{E_2}{E_1} = 2 $

$ \displaystyle E_2 = 2 E_1 $

$ \displaystyle E_2 = 2\times 6.21 \times 10^{-21}$

$ \displaystyle E_2 = 12.42 \times 10^{-21} J $