Isothermal process

A thermodynamic process in which the temperature of the system stays constant; $\Delta T=0$. Assuming that the quantity n of moles of gas of the system also remains constant, then the internal energy E of the system also remains constant, viz.

$\Delta E=nR\Delta T=0$,

but this means, according to the ideal gas law, that

$\Delta (PV)=0$

so that

$P_{i}V_{i}=PV=P_{f}V_{f}$

where $P_{i}$ is the pressure of the initial state, $V_{i}$ is the volume of the initial state, $P_{f}$ is the pressure of the final state, $V_{f}$ is the volume of the final state, and P and V are the pressure and volume of an intermediate state of the isothermal process.

An isothermal process is shown as a hyperbolic line (T₀ = constant) on a P-V (Pressure-Volume) diagram which asymptotically approaches both the V (abcissa) axis and the P (ordinate) axis. The line is called an isotherm and its equation is

$P={n_{0}RT_{0} \over V}.Accordingtothe[[firstlawofthermodynamics]],theisothermcanbedescribedalsobytheequation:<math>Q=W$

where W is work done by the system. This means that, during an isothermal process, all heat accepted by the system from its surrounds must have its energy entirely converted to work which it then performs on the surroundings, so that all the energy which comes into the system then comes right back out of the system so the internal energy (and thus the temperature) of the system remains constant.