Question

At what temperature pressure remaining constant will the r.m.s velocity of a gas be half of its value at $0^{0}C$

• A. $-{20}^{0}C$
• B. $-{190}^{0}C$
• C. $-{130}^{0}C$
• D. $-{204}^{0}C$

Answer 1

The correct option is D $-{204}^{0}C$

$V_{rms}$ $\propto$ $\sqrt{T}$
At $0^{0}C$, $V_{rms}$ $\propto$ $\sqrt{273}$
At temp. T, $\frac{V_{rms}}{2}$ $\propto$ $\sqrt{T}$
$\therefore$ $\frac{1}{2}$ = $\frac{\sqrt{T}}{\sqrt{273}}$
$T=\frac{273}{4}$ = $68.2K$ = $69K$
$T=69-273$ = $-{204}^{0}C$