Question

$\huge{\underline{\sf{\green{Proof:-}}}}$
Cp-Cv= R​

Answer 1

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Answer 2

Answer:

For an ideal gas, internal energy(U) and enthalpy(H) are functions of temperature(T) only , due to the ASSUMPTION of very low inter molecular forces between atoms/molecules . Therefore, specific heats at constant volume and pressure may be defined as follows, without resorting to partial derivatives.

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

Explanation: