Question

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

• A. 516 m/s
• B. 450 m/s
• C. 310 m/s
• D. 746 m/s

Answer 1

Answer: (A)

We know that rms speed is directly proportional to square root of temperature.
$v_{ rms } \propto \sqrt{T}$
Hence, $\frac{v_{ rms }(1)}{v_{ rms (2)}}=\sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{400}{v_{ rms (2)}}=\frac{\sqrt{27+273}}{\sqrt{227+273}}$
$=\sqrt{\frac{300}{500}}$
$v_{ rms (2)}=v=\sqrt{\frac{500}{300}} \times 400$
$=1,29 \times 400=516.39\, m / s$
$\approx 516\, m / s$