Isentropic process (temperature and pressure relationship)

[yecko]

Homework Statement

for isentropic process, which of the following is true about the relationship of temperature and pressure?

(1): P2/P1=(T2/T1)^[γ/(γ-1)]
(2): P2/P1=(T2/T1)^[(γ-1)/γ]

where γ = 1.4 for air

Homework Equations

stated above

The Attempt at a Solution

I have found equation (1) in my module lecture notes and both equation (1) and (2) in my textbook.

Let me attached the image of the related part of the textbook here:
For (1): https://i.imgur.com/Z7vPTWX.png

For (2): https://i.imgur.com/nsrmUL0.png

I feel like they are giving out different answer and I am not sure which one is true or which implies in what specific condition.
Thank you very much!

 

[kuruman]

Perhaps you can derive the correct expression yourself. Hint: Use the ideal gas law to eliminate the pressure in the isentropic expression pV^γ = constant.

 

[yecko]

I remember our lecturer had derived the equation during lecture and what she got is this.

(1): P2/P1=(T2/T1)^[γ/(γ-1)]

Do you think the other equation (i.e. P2/P1=(T2/T1)^[(γ-1)/γ] ) is wrong?
Thanks.

 

[kuruman]

I think that one of the two equations is a typo. Can you figure out which one? Just reconstruct your lecturer's derivation as I outlined in post #2.