Question

Derive cp and cv and establish the relation cp-cv=r

Answer 1

For ideal gas, internal energy(U) and enthalpy(H) are functions of temperature(T) ONLY ,due to assumption of very low inter molecular forces between molecules . Specific heats at constant volume and pressure are defined as follows.

C(v) =dU/dT…………..…………(1)

C(p)=dH/dT……………………..(2)

H=U+PV…………………………..(3)

PV=RT (ideal gas law)………..(4)

Differentiating (3)&(4) wrt temperature and substituting (1)&(2)we get,

dH/dT=dU/dT +d(PV)/dT

C(p)=C(v)+R

C(p)-C(v)=R