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 (v=c) process from P-v into T-s. See Image.
Slope of constant volume line on T-s diagram = T/Cp
This knowledge will be all to convert isometric (p=c) process 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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