Question

The rms speed of he gas atom is 5/7 of the rms speed of H${}_2$ gas molecules. If the temperature of H${}_2$ gas be 0${}^o$C, then the temperature of He will be approximately

• A. ${273}^o$C
• B. $100K$
• C. $0^o$C
• D. $0K$

Answer 1

Answer: (C)

$0^o$C

Given that $V_{rms}$of Helium =$\frac{5}{7}$times of $V_{rms}$of Hydrogen gas

$\sqrt{\frac{3RT}{4}}=\frac{5}{7}\times \sqrt{\frac{3R\times 273}{2}}$ (used the standard formula)

$\frac{3RT}{4}=\frac{25}{49}\times \frac{3R\times 273}{2}$

$T=\frac{25}{49}\times 273\times 2$

=278.571K

$\approx 273K=0^{0}C$