Why does the Second Law impose a limit on the efficiency of a heat engine?
**Adiabatic process** no heat exchange Q=0, first law ΔU = -W, for ideal gas P V^γ = constant, T V^{γ-1}= constant, P^{1-γ} T^{γ}= constant, γ = C_p/C_v = (f+2)/f, monatomic γ=5/3, diatomic γ=7/5. Work done W = (P₁V₁ - P₂V₂)/(γ-1), temperature changes due to work. The Second Law (e.g., Kelvin-Planck) requires some heat to be rejected to a cold reservoir, preventing complete conversion of heat to work. This inherent loss sets a maximum efficiency below 100%, dependent on temperature difference. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁),
Ref: NCERT > Physics Book > Thermodynamics > Adiabatic Processes and Gamma Determination