How to derive Mayer's formula i.e. Cp-Cv = R

You know the first law of thermodynamics?



(when pressure constant)

(when pressure constant)

(negative since work is done by the gas)

Now, what is ?

for one mole of gas

Since pressure is constant, and R is a constant, a change in V will cause a change in T.



Substitute in the first law of thermodynamics:



Divide by delta T:



Make R the subject: