Question

proof of Meyer's law cp-cv=r

Answer 1

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Answer 2

let dQ amount of heat supplied to (system) container keeping volume constant as a result its temperature change from T1 to T2
then from conservation of energy ,
W=pdv=0
(dQ) v=dU+ W
(dQ) v=dU -----------(1)
let dQ heat supplied to system keeping pressure constant as a result its temperature change T1 to T2
(dQ)p =dU +dW
dU +pdV----------(2)
since change in temperature both cases are same , hence change in internal energy are also same
hence ,
from equation (1) and (2)
(dQ)p =(dQ) v +dW ----------(3)
as we know
pv=nRT
differentiate
pdv +vdp =nRdT
but p =const
so, vdp =0
hence pdV=nRdT
now use this in equation (3)
(dQ) p=(dQ) v +nRdT
(dQ)p/ndT -(dQ)v/ndT=R
Cp -Cv =R