Derive the relationship between `C_(p) and C_(v)` for an ideal gas.

Explanation

Relation between Cp and Cv for an ideal gas . From the definition of enthalpy
`H = U + PV " " . . . . (1)`
For 1 mole of an ideal gas
`PV = nRT " " . . . . (2)`
By substituting (1) in (2)
`H = U + nRT " " . . . . (3)`
Differentiating the above equation with respect to
` T , (del H)/(delT) = (delU)/(delT) + "nR"(delT)/(delT)`
` [ :' ((delH)/(delT))_(p)=D_(p)and ((delU)/(delT))_(v)=C_(V)]`
`C_(p) = C_(v) +nR`
`C_(p) - C_(v) = nR`