Lesson 7 of 13 · 6 min
Quasi-static and isothermal processes
NCERT §11.8.1, §11.8.2
To compress gas gently, Vikram loads a piston with a heap of fine sand and then removes the grains a pinch at a time. Riya asks why he doesn't just lift the weight off.
The lesson in notes
In short
If the external pressure on a gas is suddenly reduced (say a weight is lifted off the piston), the piston accelerates outward and the gas passes through non-equilibrium states without a defined pressure or temperature. A finite temperature difference with the surroundings likewise causes a rapid, non-equilibrium heat exchange.
A quasi-static ('nearly static') process is an idealised, infinitely slow process in which the system stays in thermal and mechanical equilibrium with its surroundings at every stage. The pressure and temperature of the surroundings differ from the system's only infinitesimally.
To reach (P′, T′) from (P, T) quasi-statically: change the external pressure by a tiny amount, let the gas equalise, and repeat; for temperature, use a series of reservoirs whose temperatures differ from the gas by tiny amounts, running from T to T′.
It is a hypothetical construct, but slow processes without accelerating pistons or large temperature gradients come close to it. From here on, processes are taken to be quasi-static unless stated otherwise.
Table 11.2 special processes: isothermal (temperature constant), isobaric (pressure constant), isochoric (volume constant), adiabatic (no heat flow between system and surroundings, ΔQ = 0).
An isothermal process: a gas expanding in a metal cylinder placed in a large reservoir at fixed temperature. The reservoir's huge heat capacity keeps its temperature essentially unchanged as it gives or takes heat.
For an ideal gas at fixed T, PV = constant (Boyle's law): the pressure of a given mass varies inversely as its volume.
Work in an isothermal change from V₁ to V₂: W = ∫P dV = μRT ∫dV/V = μRT ln(V₂/V₁).
U of an ideal gas depends only on T, so ΔU = 0 and Q = W. Expansion (V₂ > V₁): W > 0, the gas absorbs heat and does work. Compression (V₂ < V₁): W < 0, work is done on the gas and it gives out heat.
Heat can flow in an isothermal quasi-static process even though the gas is always at the reservoir's temperature, because an infinitesimal temperature difference is enough to drive it.