Question

The average translational energy and the rms speed of molecules in a sample of oxygen gas at $300K$ are $6.21\times 10^{-21}J$ and $484m{s}^{-1}$ respectively. The corresponding values of $600K$, are nearly (assuming ideal gas behaviour)

• A. $12.42\times 10^{-21}J,968m{s}^{-1}$
• B. $8.78\times 10^{-21}J,684m{s}^{-1}$
• C. $6.21\times 10^{-21}J,968m{s}^{-1}$
• D. $12.42\times 10^{-21}J,684m{s}^{-1}$

Answer 1

Answer: (D)

Using $\overline{KE}=\frac{3}{2}kT$ and $v_{rms}=\sqrt{\frac{3kT}{m}}$, we get $\frac{{\overline{KE}}_{600}}{{\overline{KE}}_{300}}=\frac{600}{300}=2$ $i.e.$ ${\overline{KE}}_{600}=2\times 6.21\times 10^{-21}$ = 12.42 $\times 10^{21}$ J $\frac{v_{rms600}}{v_{rms300}}\sqrt{\frac{600}{300}}=\sqrt{2}$ $i.e.$ $v_{rms600}=\sqrt{2}\times 484=684.4m{s}^{-1}$