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

Step-by-step 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 ((V)/(2)\right )`

`P_2`=337.066KPa

`V_2`=
`0.493* 10^(-3) m^(3)`

and entropy is given by

`\Delta s`=
`C_v \ln \left ((P_2)/(P_1)\right )`+
`C_p \ln \left ((V_2)/(V_1)\right )`

Where,
`C_v`=
`(R)/(\gamma-1)`=0.6059

`C_p`=
`(\gamma R)/(\gamma -1)`=0.9027

Substituting values we get

`\Delta s`=
`0.6059*\ln \left ((337.066)/(120)\right )`+
`0.9027 \ln \left ((1)/(2)\right )`

`\Delta s`=-0.4199 J/k