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Ummeed · Oct 6, 2009, 04:37 AM

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

Unknown008 · Oct 6, 2009, 07:33 AM

You know the first law of thermodynamics?

$\Delta U = \Delta Q + \Delta W$

$\Delta U = c_v \Delta T$ (when pressure constant)

$\Delta Q = c_p \Delta T$ (when pressure constant)

$\Delta W = -P\Delta V$ (negative since work is done by the gas)

Now, what is $-P\Delta V$ ?

$PV = RT$ for one mole of gas

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

$P\Delta V = R\Delta T$

Substitute in the first law of thermodynamics:

$c_v \Delta T = c_p \Delta T- R\Delta T$

Divide by delta T:

$c_v = c_p - R$

Make R the subject:

$c_p - c_v = R$