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(D) The pressure $P$ of an ideal gas is given by the kinetic theory as $P = \frac{1}{3} \frac{N m}{V} v_{rms}^2$. Since the average kinetic energy of

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(D) The pressure $P$ of an ideal gas is given by the kinetic theory as $P = \frac{1}{3} \frac{N m}{V} v_{rms}^2$. Since the average kinetic energy of a molecule is $\frac{1}{2} m v_{rms}^2 = \frac{3}{2} k_B T$,we have $v_{rms}^2 \propto T$. The force $F$ exerted by a molecule on the wall is proportional to the rate of change of momentum,which is proportional to the square of the velocity $(F \propto v^2)$. Since $v_{rms}^2 \propto T$,it follows that the force $F \propto T^1$. Comparing this with $F \propto T^q$,we get $q = 1$.

In an ideal gas at temperature $T,$ the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is

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