Answer
$W = 2.56 kJ$
Work Step by Step
Assuming that the nitrogen is an ideal gas:
$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} $
With:
$P_1 = 130 kPa, P_2 = 100kPa, V_1 = 0.07 m³$
$T_1 = 120°C + 273.15 = 393.15 K, T_2 = 100°C + 273.15 = 373.15 K$
$V_2 = 0.0864 m³$
Therefore:
$P_1V_1^n = P_2V_2^n \rightarrow \ln(\frac{P_1}{P_2}) = n\ln(\frac{V_2}{V_1})$
$n = 1.25$
The work for a polytropic process is given by:
$W = \frac{P_2V_2-P_1V_1}{1-n}$
$W = 2.56 kJ$
