Answer
$W_{sh}=-44.85\ Btu$
Work Step by Step
For an ideal gas:
$PV=mRT$
Plugging in the values:
$P_1=14.7\ psia, V_1=V_2=10\ ft³, T_1=80°F=539.67°R, R=0.3353\ psia.ft³/lbm.°R$
We get to $m=0.812\ lbm$
In the final state ($P_2=20\ psia$):
We get to $T_2=734.58°R$
The energy balance for the system:
$Q-W_{sh}=\Delta U = mc_v\Delta T$
Plugging in the values of $Q=-20\ Btu, c_v=0.157\ Btu/lbm.°R$
$W_{sh}=-44.85\ Btu$
