What is the relationship between C_p and C_v for an ideal gas?
**Carnot engine** reversible engine operating between T_h and T_c has maximum efficiency η =1 - T_c/T_h, T in kelvin, e.g., T_h=400 K T_c=300 K η=0.25, real engines less due to irreversibilities, second law defines direction of spontaneous processes and entropy increase. For an ideal gas, the molar specific heat at constant pressure ( C_p ) exceeds that at constant volume ( C_v ) by the gas constant ( R ), due to the work done during expansion at constant pressure: C_p - C_v = R . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal
Ref: NCERT > Physics Book > Thermodynamics > Second Law Heat Engines and Kelvin-Planck