Answer
(a) The kinetic energy per unit volume is $1.52\times 10^5~J/m^3$
(b) The kinetic energy per unit volume is $4.55\times 10^7~J/m^3$
Work Step by Step
(a) The total translational kinetic energy is the number of molecules $N$ multiplied by the average translational kinetic energy of the molecules $\overline{KE}$. We can find the kinetic energy per unit volume:
$N\times~\overline{KE} = \frac{3}{2}~NkT$
$KE = \frac{3}{2}~PV$
$\frac{KE}{V} = \frac{3}{2}~P$
$\frac{KE}{V} = \frac{3}{2}~(1.01\times 10^5~Pa)$
$\frac{KE}{V} = 1.52\times 10^5~J/m^3$
The kinetic energy per unit volume is $1.52\times 10^5~J/m^3$
(b) We can find the kinetic energy per unit volume at $P = 300.0~atm$:
$N\times~\overline{KE} = \frac{3}{2}~NkT$
$KE = \frac{3}{2}~PV$
$\frac{KE}{V} = \frac{3}{2}~P$
$\frac{KE}{V} = \frac{3}{2}~(300.0)(1.01\times 10^5~Pa)$
$\frac{KE}{V} = 4.55\times 10^7~J/m^3$
The kinetic energy per unit volume is $4.55\times 10^7~J/m^3$
