JEE MAIN - Physics (2023 - 24th January Morning Shift - No. 15)
Given below are two statements :
Statement I : The temperature of a gas is $$-73^\circ$$C. When the gas is heated to $$527^\circ$$C, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the option given below :
Statement I is true but Statement II is false
Both Statement I and Statement II are true
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Explanation
$T_{i}=200 \mathrm{~K} \quad\quad v_{\mathrm{rms}} \propto \sqrt{T}$
$T_{f}=800 \mathrm{~K}$
$\frac{V_{i}}{V_{f}}=\sqrt{\frac{T_{i}}{T_{f}}}=\sqrt{\frac{200}{800}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
$V_{f}=2 V_{i}$
Translational K.E. $=\left(\frac{3}{2} P V\right)$
$T_{f}=800 \mathrm{~K}$
$\frac{V_{i}}{V_{f}}=\sqrt{\frac{T_{i}}{T_{f}}}=\sqrt{\frac{200}{800}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
$V_{f}=2 V_{i}$
Translational K.E. $=\left(\frac{3}{2} P V\right)$
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