(HL) Thermodynamics, entropy and heat engines

Learning objectives

(HL) Apply the first law of thermodynamics Q = ΔU + W, using the sign convention in which Q is the energy transferred to the gas and W is the work done by the gas

(HL) Calculate the work done by an expanding gas from W = pΔV at constant pressure, and from the area under the curve on a pressure–volume diagram for any process

(HL) Describe isovolumetric, isobaric, isothermal and adiabatic changes, and apply pV^(5/3) = constant to an adiabatic change of a monatomic ideal gas

(HL) Define entropy, calculate the entropy change of a reservoir from ΔS = ΔQ/T, and state the second law of thermodynamics as the requirement that the entropy of an isolated system cannot decrease

(HL) Apply S = kB ln Ω, relating entropy to the number of microstates Ω of a system, and calculate a change in entropy from ΔS = kB ln(Ω₂/Ω₁)

(HL) Analyse a cyclic process on a pressure–volume diagram, calculating the net work done per cycle and the thermal efficiency η = W/QH

(HL) Compare a real heat engine with the Carnot cycle, and calculate the maximum theoretical efficiency from ηCarnot = 1 − Tcold/Thot