Equilibrium, heat and the first law

Thermodynamics ('heat in motion') studies how heat and work change the energy of a whole system, such as a gas in a cylinder. It does not look at single molecules (that is kinetic theory); it uses a few measurable state variables: pressure P, volume V, temperature T, and the amount of gas.

Two kinds of wall matter. An adiabatic wall lets no heat through, so two gases on either side keep their own temperatures. A diathermic wall (a thin metal sheet) lets heat through, and the two sides end up at the same temperature: they are in thermal equilibrium.

Zeroth law: if A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This is what makes a thermometer work: C is the thermometer, and the quantity that comes out equal is temperature.

Internal energy U is the total kinetic and potential energy of the molecules' disordered motion inside the system (not the motion of the system as a whole). It depends only on the state: bring a gas back to the same P, V and T, and its U is the same again, whatever happened in between.

Heat and work are two different ways of changing U, not things a system 'has'. Heat flows because of a temperature difference; work is done when, say, the gas pushes a piston out.

First law (conservation of energy): ΔQ = ΔU + ΔW.

• ΔQ = heat supplied to the system (+), ΔU = rise in internal energy (+), ΔW = work done by the system (+). Heat given out or work done on the gas count as negative.
• For a gas, the work is ΔW = PΔV (more precisely ∫P dV).
• Example: a gas takes in 500 J of heat and pushes a piston out with 200 J of work. Its internal energy rises by 500 – 200 = 300 J.

For an ideal gas, U depends only on T. So in an isothermal process (T fixed) ΔU = 0, and all the heat taken in comes out as work: ΔQ = ΔW.