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