Answer
$W = -5.14\ BTU$
Work Step by Step
Since we're given the P-V diagram, the work is the are under the curve:
$W_{1-2} = (V_2 - V_1)\frac{P_2+P_1}{2}$
$W_{2-3} = (V_3 - V_2)P_3$
With
$V_1 =1 ft³, V_2 = 3.3 ft³, V_3 = 2 ft³, P_1 = 15\ psia, P_2=P_3 = 300\ psia$
$c_1 = 144 \frac{psf}{psi}, c_2 = \frac{1\ BTU}{778.2\ lbf.ft}$
$W_{1-2} = (2.3 ft³)157.5psi \times c_1c_2 = 67.03 BTU$
$W_{2-3} = (-1.3ft³)300 psia \times c_1c_2 = -72.16 BTU $
$W = W_{1-2} +W_{2-3} $
$W = -5.14\ BTU$
