Shortcuts to convert P-v diagram into T-s diagram

Most of you might have faced problems while converting P-v diagram into T-s diagram. In this post I will be sharing some shortcuts using which you can easily convert any P-v diagram into T-s diagram.

I am starting with basic process and then discuss polytropic process in the end.

1. Isothermal process:

Note that constant temperature line is drawn such that entropy has decreased. Why? Why not along increasing entropy? Keep this funda in mind that increase/decrease in entropy in T-s diagram is determined only by a single phenomenon : Heat addition/rejection.

If heat is being added, entropy will increase. If heat is being rejected, entropy will decrease. 1 – 2 is compression still temperature is same. Using first law, this is possible only if the system is rejecting heat, so entropy should also decrease.

2. Isentropic process:

Note that constant entropy (rev adiabatic) line is drawn such that temperature has increased. Why? Why not along decreasing temperature? You have to see this from the process on P-v. It is an adiabatic compression, so T will increase. If it was adiabatic expansion, T would have decreased.

3. Constant volume process:

Slope of constant volume line on T-s diagram = T / Cv.

This knowledge will be all to convert isometric process (v=constant) from P-v into T-s diagram. See Image.

4. Constant pressure process:

Slope of constant volume line on T-s diagram = T/Cp

This knowledge will be all to convert isobaric process (p=constant) from P-v into T-s. See Image.

Note that on T-s diagram, slope of constant volume line is more than slope of constant pressure since T/Cv > T/Cp

5.  Polytropic process:

Use the funda of polytropic specific heat in determining this.

 • Case A: if n is in the range of 1 to ϒ, polytropic specific heat will be –ve.
From the relation Q = mcΔT, if c is negative, increase in T will decrease Q (so decrease entropy) and decrease in T will increase Q (so increase entropy)

• Case B: if n > ϒ, polytropic specific heat will be +ve.
From the relation Q = mcΔT, if c is positive, increase in T will increase Q (so increase entropy) and decrease in T will decrease Q (so decrease entropy).
It means if n>gamma, then T and S will have same characteristic.

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