2.) An ideal monatomic gas is slowly taken from $P_1$, $V_1$, $T_1$, to $P_2$, $V_2$, $T_2$. Match the work done on the gas with the conditions.

a.) Constant pressure	ii) $$P_1(V_1-V_2)$$
b.) Constant volume	iv) 0
c.) Constant temperature	i) $$n R T_1 \ln\left(\frac{V_1}{V_2}\right)$$
d.) Constant entropy	iii) $$\frac 3 2 n R(T_2-T_1)$$

Comments:
a.) Work done = $-\int P {\rm d}V$ = $-P\Delta V$ for constant $P$.
b.) Work done = $-\int P {\rm d}V$ so it's obviously zero if $V$ doesn't change!
c.) Obtained by substituting $P=nRT/V$ and taking the constant $T$ out of the integral.
d.) Constant entropy means no heat flow so $W=\Delta E=C_{\scriptscriptstyle V}\Delta T$ and $C_{\scriptscriptstyle V}=3nR/2$.
See section and examples on work.

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