Which of the following represents the slope of constant pressure line on T-s diagram of an ideal gas? (where, $C_{p}$ and $C_{v}$ are specific heat
at constant pressure and specific heat at constant volume respectively)

Question

Question

This question was previously asked in

SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

Combined equations of the first and second law of thermodynamics

Tds = du + Pdv

Tds = dh – vdP

These equations are applicable for both reversible and irreversible process and for the closed and open system as well.

du = CvdT

dh = CpdT

Cv = specific heat at constant volume, Cp = specific heat at constant pressure

From second equation

Tds = dh – vdP

For constant pressure, dP = 0 & dh = CpdT

Tds = CpdT

Hence on the T-S diagram, the slope of the constant pressure line = T/Cp

Additional Information

From first equation

Tds = du + Pdv

For constant volume, dv = 0

And, du = CvdT

∴ 1st equation becomes: Tds = CvdT