A compressor undergoes a reversible, steady flow process.

Home » Thermodynamics » Thermodynamics Miscellaneous » Question

A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state 1 and state 2 respectively. Potential and kinetic energy changes are to be ignored. The following notations are used: v = specific volume and P = pressure of the gas. The specific work required to be supplied to the compressor for this gas compression process is

1. ∫²₁ Pdv
2. ∫²₁vdP
3. v₁ (P₂–P₁)
4. –P₂ (v₁– v₂)

Correct Option: B

h = u + Pv
⇒ dh =du + Pdv + vdP
But dQ =du + Pdv
∴ du = dQ –Pdv
∴ dh = dQ – Pdv + Pdv + vdP
⇒ dh = dQ + vdP
⇒ –vdP = d(P.E) + d(K.E) + dW
Since K.E and P.E are constant
∴ dW = ∫²₁vdP