prove that cp-cv=r

My ans is 4

How can your answer be 4 if it asks you to prove something? :rolleyes:

I have a link where I proved this some months ago:

https://www.askmehelpdesk.com/physics/proof-cp-cv-r-438863.html#post2566584

If you have something to say, post in your thread and not there please.

Consider a thermodynamic process in which a gas is heated.
Case 1:constant volume:
DU=Q+dW
Here dW = 0
Hence dU=Q=Cp.dT... (1) (from definition)

Case 2:at constant pressure, gas is heated so that the same change in internal energy takes place.
Then dU = Q + dW
Q = Cv.dT
Hence dU = Cv.dT + R.dT (dW = p.dV = R.dT)
Substituting from (1), we get
Cp.dT = Cv.dT + R.dT
=>Cp = Cv + R,
Which is the required result