Lesson 2 of 13 · 6 min
Thermal equilibrium and the zeroth law
NCERT §11.2, §11.3
The workshop has a steel water tank and a copper coolant jug, both sitting in the shade since morning. Riya has one small digital thermometer and wonders whether the tank and the jug are at the same temperature without pouring one into the other.
The lesson in notes
In short
In mechanics, equilibrium means zero net external force and torque. In thermodynamics, a system is in equilibrium when its macroscopic variables stay constant in time, e.g. a gas in a closed, rigid, fully insulated container with fixed P, V, T, mass and composition.
Whether a system reaches equilibrium depends on its surroundings and on the wall between them. An adiabatic wall is insulating: it lets no heat through. A diathermic wall is conducting: heat can flow across it.
Two gases A and B separated by an adiabatic wall: any pair of values (P_A, V_A) can sit in equilibrium with any pair (P_B, V_B). Replace the wall with a diathermic one and the variables of both change on their own until each settles to a new steady state; then no more energy flows. A and B are now in thermal equilibrium.
Not every variable has to change. If both gases are in fixed-volume containers, only their pressures change on the way to 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. Test: let A and B each reach equilibrium with C through conducting walls, then put a conducting wall between A and B and insulate C; the states of A and B do not change further.
R. H. Fowler put this law into words in 1931, long after the first and second laws had been stated and numbered, hence the name 'zeroth'.
The zeroth law says there is a quantity that has the same value for any two systems in thermal equilibrium. That quantity is temperature T: if T_A = T_C and T_B = T_C, then T_A = T_B.
So the zeroth law gives the formal basis of temperature; thermometry then deals with putting numbers on it.