In class, we saw the following expression for how the internal energy of a gas changes as the volume changes at constant temperature:

$($U$$V$)$T$=\backslash$mu J$$TCP$+$V$\backslash$kappa V$$P

Using this formula, we can find the change in internal energy of the gas by multiplying both sides by dV and integrating:

$\backslash$Delta U$=$V$2$V$1(\backslash$mu J$$TCP$+$V$\backslash$kappa V$$P$)$dV

If we assume that the gas behaves ideally when we determine the pressure, we end up with:

$\backslash$Delta U$=$V$2$V$1(\backslash$mu J$$TCP$+$V$\backslash$kappa V$$nRTV$)$dV

What is $\backslash$Delta U

for $0\mathrm{.}5$ moles of a gas which goes from a state of $(0\mathrm{.}6$ m$3,212$ K$)$ to a state of $(1\mathrm{.}3$ m$3,212$ K$),$ if it has the following properties?

You may approximate that the following properties are constant under these conditions.

$\backslash$mu J$$T

$=8\mathrm{.}7$E$-6$ K$/$Pa

CP

$=0\mathrm{.}34$ J$/$K

$\backslash$kappa

$=4\mathrm{.}4$E$-5$ Pa$-1$