Question

A piston-cylinder device contains 1.329 kg of nitrogen gas at 120 kPa and 27 degree C. The gas is now compressed slowly in a polytropic process during which PV^1.49 = constant. The process ends when the volume is reduced by one-half. Determine the entropy change of nitrogen during this process.

Answer 1

Answer:-0.4199 J/k

Explanation:

Given data

mass of nitrogen(m)=1.329 Kg

Initial pressure$\left ( P_1\right )$=120KPa

Initial temperature$\left ( T_1\right )=27\degree \approx$ 300k

Final volume is half of initial

R=particular gas constant

Therefore initial volume of gas is given by

PV=mRT

V=0.986\times 10^{-3}

Using $PV^{1.49}$=constant

$P_{1}V^{1.49}$=$P_2\left (\frac{V}{2}\right )$

$P_2$=337.066KPa

$V_2$=$0.493\times 10^{-3} m^{3}$

and entropy is given by

$\Delta s$=$C_v \ln \left (\frac{P_2}{P_1}\right )$+$C_p \ln \left (\frac{V_2}{V_1}\right )$

Where, $C_v$=$\frac{R}{\gamma-1}$=0.6059

$C_p$=$\frac{\gamma R}{\gamma -1}$=0.9027

Substituting values we get

$\Delta s$=$0.6059\times\ln \left (\frac{337.066}{120}\right )$+$0.9027 \ln \left (\frac{1}{2}\right )$

$\Delta s$=-0.4199 J/k