MCQ
One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by factor.
- A$1.5$
- B$\sqrt 2 $
- C$2$
- ✓$4$
$\mathrm{v}_{\mathrm{rms}}=1.085 \mathrm{v}_{\mathrm{avg}}$
$\Rightarrow \sqrt{\frac{3 P}{\rho}}=1.085 \mathrm{v}_{\mathrm{avg}} ; \rho$ is density
In this case $\rho$ is constant
$\therefore P \propto\left(V_{\text {avg }}\right)^{2}$
$\therefore \frac{P_{f}}{P_{i}}=\left[\frac{\left(v_{\text {avg }}\right)_{f}}{\left(v_{\text {avg }}\right)_{i}}\right]^{2}=4$
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