JEE Physics

Maximum efficiency (Carnot efficiency) = 1 - (T_cold/T_hot) = 1 - (300/500) = 1 - 0.6 = 0.4 = 40%

First law: ΔU = Q - W, so W = Q - ΔU = 8000 - 5000 = 3000 J (work done by the system)

By first law of thermodynamics: ΔU = Q - W = 2400 - 600 = 1800 J (where W is work done by system)

For an ideal gas, internal energy U depends only on temperature (U = nC_vT). This is independent of pressure or volume, as shown by kinetic theory.

For adiabatic process: PV^γ = constant, TV^(γ-1) = constant, and T^γ P^(1-γ) = constant. All three relations are equivalent and correct.

First law: ΔU = Q - W = 4000 - 1500 = 2500 J (where W is work done by system)

Carnot efficiency η = 1 - T_cold/T_hot = 1 - 300/400 = 0.25 = 25%

Internal energy U of ideal gas is U = nCᵥT, which depends only on temperature, not on pressure or volume individually

For adiabatic process: TV^(γ-1) = constant, therefore T₁V₁^(γ-1) = T₂V₂^(γ-1)

For isothermal process: W = nRT ln(V₂/V₁) = P₁V₁ ln(V₂/V₁) = P₀V₁ ln(2)