Question

When temperature of an ideal gas is increased from $27{^\circ}C$ to $227{^\circ}C$, its r.m.s. speed changed from 400 metre/sec to $V_{s}.$ The $V_{s}$ is

• A. 516 metre/sec
• B. 450 metre/sec
• C. 310 metre/sec
• D. 746 metre/sec

Answer 1

Answer: (A)

516 metre/sec

Answer 2

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow \frac{v_{S}}{400} = \sqrt{\frac{(273 + 227)}{(273 + 27)}} = \sqrt{\frac{5}{3}}$

$\Rightarrow v_{s} = 400\sqrt{5/3} = 516m/s$