Question

A frictionless piston-cylinder device contains 4.5 kg of nitrogen at 110 kPa and 200 K. Nitrogen is now compressed slowly according to the relation PV1.5 = constant until it reaches a final temperature of 360 K. Calculate the work input during the process, in kJ.

Answer 1

Answer:

427.392 kJ

Explanation:

m = Mass of gas = 4.5 kg

Initial temperature = 200 K

Final temperature = 360 K

R = Mass specific gas constant = 296.8 J/kgK

$\gamma$ = Specific heat ratio = 1.5

Work done for a polytropic process is given by

$W=\frac{mR\Delta T}{1-\gamma}\\\Rightarrow W=\frac{4.5\times 296.8(360-200)}{1-1.5}\\\Rightarrow W=-427392\ J\\\Rightarrow W=-427.392\ kJ$

The work input during the process is -427.392 kJ