Question

If pressure is assumed to be constant, at what temperature will the rms speed of gas molecules increase by $10\%$ of the rms speed at STP?

• A. $57.3\text{K}$
• B. $57.3{}^{\circ }\text{C}$
• C. $557.3\text{K}$
• D. $-57.3{}^{\circ }\text{C}$

Answer 1

The correct option is B $57.3{}^{\circ }\text{C}$

$v_{rms\left(T\right)}=V_{rms\left(STP\right)}+V_{rms\left(STP\right)}\frac{10}{100}$

$\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3R\left(273\right)}{M}}+\sqrt{\frac{3R\left(273\right)}{M}}\times \frac{1}{10}$

$\sqrt{T}=\sqrt{273}(1+\frac{1}{10})=\sqrt{273}\times \frac{11}{10}$

$T=\frac{121}{100}\times 273=330.3K=57.3{}^{\circ }\text{C}$