Lesson 9 of 13 · 6 min
Isochoric, isobaric and cyclic processes
NCERT §11.8.4, §11.8.5, §11.8.6
A sealed spray can lies near a hot exhaust pipe, while a balloon tied to the workshop fan warms in the sun. One cannot change its volume; the other keeps its pressure near atmospheric and swells.
The lesson in notes
In short
Isochoric (V constant): the gas neither does work nor has work done on it. All the heat absorbed goes into internal energy and raises the temperature; the rise for a given heat is set by the specific heat at constant volume.
Isobaric (P constant): the gas does work W = P(V₂ − V₁) = μR(T₂ − T₁).
In an isobaric process the temperature changes, so U changes too. The heat absorbed goes partly into internal energy and partly into work; the temperature rise for a given heat is set by the specific heat at constant pressure.
That is why C_p > C_v: at constant pressure part of the heat leaves as work, so more heat is needed for the same temperature rise.
Cyclic process: the system returns to its initial state. U is a state variable, so ΔU = 0 over a cycle, and the net heat absorbed equals the net work done by the system.
On a P–V diagram the work in a process is the area under its curve; for a cycle, the net work is the area enclosed by the loop.
Summary of the first law in the four special processes: isothermal ΔU = 0, Q = W; adiabatic Q = 0, W = −ΔU; isochoric W = 0, Q = ΔU; isobaric Q = ΔU + PΔV.