download the exercise with solution: isentropic process 1

A cylinder is enclosed by a piston and filled with 3.2 kg air. The air inside the cylinder is compressed isentropically from the initial state (p₁=1.4 bar, T₁=483K) to final state with pressure p₂=9.8 bar. Please determine

1) the final temperature T₂

2) the work input necessary to compress the air to final state

The heat capacity ratio is κ=1.4.

The air is assumed to be ideal gas and its specific gas constant is R=287 J/kg∙K

Solution:

1) Since the process of compression is p^1-κ· T^κ=const. Then:

2) The work for volume change (here the work input):

Also according to the properties relation of isentropic process:

Therefore we can rewrite the work for volume change: