Question
Derive a relationship between Cp and Cv for an ideal gas.
Solution
Heat (q) at constant volume is given as
Heat (q) at constant pressure is given as
But
H = U + PV
and PV = RT [for one mole of an ideal gas]
Heat (q) at constant pressure is given as
But
H = U + PV
and PV = RT [for one mole of an ideal gas]
Substituting the values of ∆H and ∆U in eq. (1), we get,
Cp∆T – Cv ∆T = R∆T or Cp – Cv = R (for one mole of an ideal gas)
Thus Cp is greater than Cv by the gas constant R i.e. approximately 2 calories or 8.314 Joules.
