# Isochoric, isobaric, isothermal and adiabatic processes

A2

We come across the definitions of these terms at A level:

Iscochoric: at constant volume (or isovolumetric)

Isobaric: at constant pressure

At A2 we take both isothermal and adiabatic to mean at constant temperature.

University

In fact, isothermal means the temperature remains constant, and adiabatic means that there are no heat transfer processes.

All four processes can be presented on a p-V graph (the blue lines are isotherms – lines showing the points at the same temperature):

The definitions mean that more is true.

 Implications for the first law Isochoric constant volume dV = 0, so W = pdV = 0 ΔU = Q Isobaric constant pressure W = pdV = p(V2 – V1) Isothermal constant temperature ΔU = 0 Q = W Adiabatic no heat transfer Q = 0 ΔU = W

From the first law of thermodynamics:

Substitute in the definitions of heat capacity and work:

Rearrange, using the ratio of heat capacities:

Integrate:

This also means that:

using the ideal gas equation to replace T.

Also from the ideal gas equation we get:

These equations are used a lot in Carnot cycles and Otto cycles.