Q$6.$ A sample consisting of $1\mathrm{.}0$mol of perfect gas molecules with $C{V}_V=20\mathrm{.}8JK-$ is initially at $3\mathrm{.}25$ atm and $310K.$ It undergoes reversible adiabatic expansion until its pressure reaches $2\mathrm{.}50$atm. Calculate the final volume and temperature and the work done.

Q$7.$ A sample consisting of $1$ mol of perfect gas atoms $($for which $\frac{?}{\text{b}\text{a}\text{r}}(C{)}_V=\frac{3}{2}R)$ is taken through the cycle shown in the following figure $($a$)$ Determine the temperature at the points $1,2,$ and $3.($b$)$ Calculate q$,$ w$,U,$ and $H$ for each step and for the overall cycle. If a numerical answer cannot be obtained from the information given, then write in$,,+-0,$ or $?$ as appropriate.