Summary table of the transformations

The four reversible transformations all arise from the same condition $\Delta S_\text{tot} = 0$, distinguished by the constraint imposed. The table collects, for each one, the characteristic constraint, the work done by the gas, the heat exchanged and the change in entropy of the gas: it is the reference scheme to keep in mind when solving a cycle made up of several segments.

Process	Constraint	$L_\text{gas}$	$Q$	$\Delta S_\text{gas}$
Isochoric	$V_B = V_A$	$0$	$nC_v\,\Delta T$	$nC_v\ln\dfrac{T_B}{T_A}$
Isobaric	$P_B = P_A$	$P\,\Delta V$	$nC_p\,\Delta T$	$nC_p\ln\dfrac{T_B}{T_A}$
Isothermal	$T_B = T_A$	$nRT\ln\dfrac{V_B}{V_A}$	$= L_\text{gas}$	$nR\ln\dfrac{V_B}{V_A}$
Adiabatic	$Q = 0$	$-\Delta E_\text{int}$	$0$	$0$

Links

Topics: Thermodynamics Concepts: Thermodynamic transformations · Entropy Skills: Solving a thermodynamic cycle · Reading graphs Objects: Ideal gas

Related exercises: Worked exercise — reversible vs irreversible isothermal expansion · Problem — Carnot cycle in the T-S plane · Ranking ΔS in three expansions