Question

What is the reversible work done if 4 m^3 of an ideal gas is compressed adiabatically pV2.5 = K from 1 Pa to 32 Pa?

(a) 18.6 J

(b) 20.4 J

(c) 24.6 J

(d) 26.2 J

This question was posed to me during an online exam.

Origin of the question is Mechanical Energy Balance topic in division Energy Balances that Include the Effects of Chemical Reaction, Ideal Processes, Efficiency and the Mechanical Energy Balance and Heats of Solution and Mixing of Basic Chemical Engineering

Answer 1

Correct answer is (a) 18.6 J

For explanation I would say: V2 = (1*4^2.5/32)^1/2.5 = 1 m^3, => W = –4∫^1pdv = –4∫^1 (32/v^2.5) dv = 18.6 J.