Govt. Exams
Entrance Exams
For Carnot refrigerator: COP = T_cold/(T_hot - T_cold) = 250/50 = 5. So W = Q_cold/COP = 1000/5 = 200 J.
For van der Waals gas, U depends on both T and V because intermolecular forces depend on volume. For ideal gas, U depends on T only.
Negative Joule-Thomson coefficient means temperature increases during throttling expansion. Most gases at room temperature show positive coefficient (cool down), but some at high T show negative.
Irreversible mixing of gases at different pressures increases total entropy of the universe (ΔS_univ > 0).
γ = Cp/Cv = 1.67. Also, Cp - Cv = R ≈ 8.314. From Cp = 30 and γ = 1.67: Cv = 30/1.67 ≈ 18 J/(mol·K). Check: 30 - 18 = 12 ≠ 8.314 (approximation issue), but ratio gives Cv ≈ 18.
For adiabatic process: T₂/T₁ = (V₁/V₂)^(γ-1) = r^(γ-1) = 16^0.4 ≈ 3.03. T₂ = 300 × 3.03 ≈ 909 K ≈ 930 K.
Joule-Thomson coefficient μ = (∂T/∂P)_H depends on gas properties. ΔT = μ × ΔP for throttling process.
Phase transition increases disorder, so entropy increases. Q = TΔS, and since T is constant and Q > 0, ΔS > 0.
Mixing is an irreversible adiabatic process. By second law, entropy of isolated system increases.
