Internal energy and thermodynamic work

When a gas expands it does work against the external pressure force; this is called thermodynamic work. For piston area S and displacement Δh, A = F·Δh = pS·Δh = pΔV, i.e. in isobaric expansion the work equals pressure times the change of volume. From the equation of state pΔV = νRΔT, so A = νRΔT; for 1 mol A = RΔT. Thus R is numerically equal to the work done when 1 mol of gas is heated by 1 K at constant pressure. When the gas expands A > 0; when external forces compress it, the gas’s work is A < 0. On a p–V graph the isobaric work equals the area of a rectangle; for an isothermal process it equals the area under the isotherm. In an isochoric process ΔV = 0, so the work is zero.