Question 879: Thermodynamics & KTG

Question

The temperature of an ideal gas is increased from $$27^{\circ} \mathrm{C}$$ to $$927^{\circ} \mathrm{C}$$. The r.m.s. speed of its molecules becomes

Accepted Answer

$$\begin{aligned}
& 	ext { We know } v_{	ext {rms }}=\sqrt{\frac{3 R T}{M}} \
& \Rightarrow \mathrm{v}_{	ext {rms }} \propto \sqrt{\mathrm{T}} \
& 	herefore \quad \frac{\mathrm{v}_{\mathrm{mm}}}{\mathrm{v}_{\mathrm{mm}_2}}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{300}{1200}}=\sqrt{\frac{1}{4}} \
& \frac{\mathrm{v}_{\mathrm{ms}}}{\mathrm{v}_{\mathrm{ms}_2}}-\frac{1}{2} \
& 	herefore \quad \mathrm{v}_{\mathrm{mss}_2}=2 \cdot \mathrm{v}_{\mathrm{rms} 1} \
&
\end{aligned}$$

Answer

twice

Answer

four times.

Answer

half.

Answer

one-fourth.

Thermodynamics & KTG

The temperature of an ideal gas is increased from $27^{\circ} \mathrm{C} to 927^{\circ} \mathrm{C}$. The r.m.s. speed of its molecules becomes

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