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(D) The pressure $P$ exerted by an ideal gas is given by the ideal gas equation $PV = N K_B T$,where $N$ is the number of molecules,$K_B$ is the Boltz

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$1$

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(D) The pressure $P$ exerted by an ideal gas is given by the ideal gas equation $PV = N K_B T$,where $N$ is the number of molecules,$K_B$ is the Boltzmann constant,and $V$ is the volume.Since pressure $P$ is defined as force $F$ per unit area $A$,we have $P = F/A$.Substituting this into the ideal gas equation:$(F/A) V = N K_B T$$F = (N K_B T A) / V$Since $N$,$K_B$,$A$,and $V$ are constants for a given container and gas sample,the force $F$ is directly proportional to the temperature $T$.$F \propto T^1$Comparing this with $F \propto T^x$,we get $x = 1$.

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 $T^{x}$. The value of $x$ is

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