Question

A piston–cylinder device initially contains 0.4 kg of nitrogen gas at 160 kPa and 140°C. Nitrogen is now expanded isothermally to a pressure of 100 kPa. Determine the boundary work done during this process. The properties of nitrogen are R = 0.2968 kJ/kg·K and k = 1.4.

Answer 1

Answer:

$W=23kJ$

Explanation:

With the respectively considerations, we calculate the initial Volume of piston cylinder,

$m=0.4Kg\\P_1=160kPa\\T=140\°c$

State 1,

$V_1 =\frac{mRT}{P_1}\\V_1 = \frac{(0.4)(0.2968)(140+273)}{160}\\V_1=0.3064$

State 2,

$V_2=\frac{mRT}{P_2}\\V_2=\frac{(0.4)(0.298)(140+273)}{100}\\V_2=0.4903m^3$

So, calculating the work done (W) relate to isothermal expansion of ideal gas

$W=P_1 V_1 ln(\frac{V_2}{V_1})\\W=(160kPa)(0.3064m^3)ln(\frac{0.4903m^3}{0.3064m^3}(\frac{1kJ}{1kPa.m^3})\\W=23kJ$