In an ideal gas at temperature T,the average | vedclass

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Question

(D) The average force $F$ exerted by a molecule on the wall of a container is given by the rate of change of momentum,$F = \frac{\Delta p}{\Delta t}$.

Vedclass · Accepted Answer

$1$

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(D) The average force $F$ exerted by a molecule on the wall of a container is given by the rate of change of momentum,$F = \frac{\Delta p}{\Delta t}$.For a molecule of mass $m$ moving with velocity $v$,the force is proportional to $\frac{mv^2}{L}$,where $L$ is the dimension of the container.From the kinetic theory of gases,the average kinetic energy of a molecule is $\frac{1}{2}mv^2 = \frac{3}{2}kT$,which implies $v^2 \propto T$.Substituting this into the force expression,we get $F \propto \frac{m(T)}{L}$,so $F \propto T^1$.Comparing this with $F \propto T^q$,we find $q = 1$.

Molecule type	$\frac{C_P}{C_V}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$

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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