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(V_{2} – V_{1}) | |
Isothermal | constant temperature | ΔU = 0 | Q = W |
Adiabatic | no heat transfer | Q = 0 | ΔU = W |
Heat capacity for adiabatic processes
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.