Answer
$P_f=3.2$ atm
Work Step by Step
We know that
$P_1V_1^{\gamma}=P_2V_2^{\gamma}$
$\implies P_2 =P_1(\frac{V_1}{V_2})^{\gamma}$............................eq(1)
Next, we calculate $\gamma$:
${\gamma=\frac{C_P}{C_V}}=\frac{\frac{5}{2}}{\frac{3}{2}}=\frac{5}{3}$
Substituting the values of $P_1,V_1,V_2$ and $\gamma$ into the formula, we get:
$P_2 =(32)(\frac{1\times10^{-3}}{4\times10^{-3}})^\frac{5}{3}$
$P_2 =3.2$ atm
Thus $P_2$ or $P_f=3.2$ atm
