First slide

Kinetic theory of ideal gases

Question

If the volume of a gas is doubled at constant pressure, the average translational kinetic energy of its molecules will

Moderate

A

be doubled
B

be halved
C

remain the same
D

become 4 times

Solution

At constant pressure,
$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \Rightarrow T_{2} = \frac{V_{2}}{V_{1}} \times T_{1} = 2 T_{1}$
Average translational kinetic energy . $= \frac{1}{2} m v_{R M S}^{2} = \frac{3}{2} \frac{R T m}{M} α (t e m p e r a t u r e)$
Since, temperature doubles, average translational KE of molecules also doubles.

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