All problems assume ideal gas $($IG$)$ behavior. $R=8\mathrm{.}3145Jmo{l}^{-1}{K}^{-1}=0\mathrm{.}082057Latmmo{l}^{-1}{K}^{-1}.$

Use J unit to report energies.

$3\mathrm{.}00$ mols of an IG are compressed isothermally at $T=415K.$ The volume of the system

is reduced by a factor of $5.$ Compute the amounts of reversible work and heat involved in

this process. What is the change of entropy of the system?

If the initial volume of the IG in Problem $1$ is $5\mathrm{.}00L,$ what is the minimum amount of

irreversible work needed to compress this IG with a constant pressure? What is that

pressure? What is the change of entropy of the system?

A sample of propane with mass $58g$ undergoes a free expansion where the gas triples

its original volume. If this happened at room temperature $(298K,$ what is the change of

entropy in this process?

$7\mathrm{.}2$ mols of $N_2$ are heated at a constant pressure of $4\mathrm{.}0$atm, where the temperature is

raised by $85K.$ The heat capacity at constant volume can be taken as $C_V=\frac{5}{2}nR.$

Compute $q,H,$ and $U.$

An IG initially occupying $5\mathrm{.}20L$ expands adiabatically, performing $1\mathrm{.}4kJ$ of work, the gas

worked against an external pressure of $1\mathrm{.}5$atm, reaching this pressure at the final

equilibrium state. The final temperature is $200K.$ What is the number of mols of the gas?