Thermodynamics: energy, work, and entropy

One mole of a monatomic ideal gas starts at V₁ = 1 L and pressure P₁. Choose a process and drag the gold end point: the curve is the exact path, and the shaded area under it is the work W = ∫P dV, positive for expansion and negative for compression. Compare how much work the same change of volume gives at constant pressure, at constant temperature and with no heat flow. The Carnot cycle joins two isotherms and two adiabats; the area it encloses is the net work, and its efficiency is 1 − Tc/Th.

A body with heat capacity C is heated from Tc to Th, either by touching one reservoir at Th (N = 1, a sudden jump) or through N reservoirs at evenly spaced temperatures. In the left graph the area under the body’s 1/T curve is its entropy gain, and the area under the staircase is the entropy the reservoirs lose. The orange slivers between them are the entropy generated. Add reservoirs and watch the slivers, and the total ΔS_univ, shrink toward zero: the reversible limit.

Change the amount, temperature and volume of an ideal gas and read the pressure. On the left, the number of molecules follows n, the box width follows V and their speed follows √T. On the right, the gold point sits on the isotherm for this temperature; drag it to change the volume. The shaded rectangle from the origin to the point has area PV, which stays equal to nRT anywhere on the isotherm.