Govt. Exams
For heat pump: COP = Q_h/W = 5000/1500 = 3.33. This indicates the pump delivers 3.33 J of heat for every 1 J of work input.
Carnot efficiency: η = 1 − (T_cold/T_hot) = 1 − (300/400) = 1 − 0.75 = 0.25 = 25%
In adiabatic compression (Q = 0), work is done on the gas (W < 0). By first law: ΔU = Q − W = 0 − W > 0. Since ΔU ∝ ΔT for ideal gas, temperature increases.
By first law of thermodynamics: ΔU = Q − W = 500 − 200 = 300 J
Carnot efficiency: η = 1 - (Tc/Th) = 1 - (300/500) = 1 - 0.6 = 0.4 = 40%
In adiabatic compression, no heat exchange occurs (Q=0). Work is done on the gas, so ΔU = W (positive). Since ΔU increases, temperature must increase.
For monatomic gas: Cv = (3/2)R and Cp = (5/2)R. Therefore Cp/Cv = (5/2)/(3/2) = 5/3 ≈ 1.67
By first law: ΔU = Q - W. Here ΔU = 150 J, W = 100 J (work done by system). So Q = ΔU + W = 150 + 100 = 250 J
For diatomic gas: Cᵥ = (5/2)R and Cₚ = (7/2)R. γ = Cₚ/Cᵥ = 7/5 = 1.40
Clausius statement: Heat cannot spontaneously transfer from a colder body to a hotter body without external work being done on the system
