Question

In one stroke of a reciprocating compressor, helium is isothermally and reversibly

compressed in a piston/cylinder from 298 K and 15 bar to 150 bar. Compute the heat
removal and work required.

Answer 1

Step-by-step explanation:

It is known that in reversible isothermal compression, relation between work and pressure is as follows.

w = -2.303 RT log
`(P_(2))/(P_(1))`

=
`-2.303 * 8.314 J/mol K * log (150 bar)/(15 bar)`

=
`-5705.85 J /mol * log (10)`

= -5705.85 J /mol

According to first law of thermodynamics, q = -w

Hence, q = -(-5705.85 J /mol)

= 5705.85 J /mol

As 1000 J = 1 kJ. Hence, convert 5705.85 J/mol into kJ/mol as follows.

`(5705.85)/(1000) kJ /mol`

= 5.7058 kJ/mol

Thus, we can conclude that heat removal is 5.7058 kJ/mol and work required is -5705.85 J /mol.