The Zeroth Law of Thermodynamics

The Zeroth Law of Thermodynamics states that if two thermodynamic systems 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 law formalizes the empirical concept of temperature and justifies the use of thermometers: a thermometer is any system that, when placed in thermal contact with another system and allowed to equilibrate, acquires a reading that can be used to characterize that system's temperature. Temperature is an intensive state variable defined by equality under thermal equilibrium; the Zeroth Law ensures the transitivity necessary to assign a single scalar temperature to equilibrium classes of systems.

Governing FormulaThere is no single algebraic equation unique to the Zeroth Law, but useful relations and definitions that rely on it include: - Thermal equilibrium transitivity: if A ↔ C and B ↔ C then A ↔ B (↔ denotes thermal equilibrium). - For a linear thermometer scale y related to absolute temperature T (Kelvin): y = a T + b (a, b constants); inversion: T = (y - b)/a. - For a resistive temperature sensor (approx. linear near a reference): R(T) = R_ref [1 + α (T - T_ref)] ⇒ T = T_ref + (R/R_ref - 1)/α. Assumptions: systems are allowed to exchange heat only (no work, no matter transfer) when establishing thermal equilibrium; thermometer reaches the same intensive property as the system.

Knowledge Check

10 Questions

1.Which statement best expresses the Zeroth Law of Thermodynamics?

2.Which thermodynamic property is appropriate to label as 'temperature' because of the Zeroth Law?

3.A single calibrated thermometer gives a reading of 295 K when placed in contact with system A and 310 K when placed in contact with system B. According to the Zeroth Law, which statement is correct?

4.A platinum resistance thermometer follows R(T)=R_ref[1+α(T-T_ref)]. Given R_ref=100.0 Ω at T_ref=273.0 K and α=0.00390 K^-1, a body in equilibrium with this thermometer gives R=132.0 Ω. What is the body's temperature (to three significant figures)? (Assume linear approximation valid.)

5.Two isolated bodies X and Y have different masses and different heat capacities, but they are prepared at the same temperature T0 and then placed in thermal contact while otherwise isolated. Immediately after contact and once equilibrium is reached, what does the Zeroth Law imply about their temperatures?

6.Two empirical temperature scales X and Y are known to be linearly related. When in equilibrium with the same reference bodies, the pairs of readings are (X=40, Y=130) and (X=100, Y=220). What is the value of Y when X reads 80?

7.Which requirement is essential for an empirical quantity to serve as a valid thermometer scale under the Zeroth Law?

8.System A is at 350 K and system B is at 300 K according to the same calibrated thermometer. They are brought into thermal contact (no work, no mass transfer). According to thermodynamic principles consistent with the Zeroth Law, which direction will net heat flow initially?

9.Which fundamental thermodynamic law justifies the operational definition of temperature using a thermometer (i.e., that a single scalar can label thermal equilibrium classes)?

10.A laboratory thermometer scale X is defined by the linear relation X = 0.01 · T (where T is absolute temperature in kelvin). If a sample in equilibrium with this thermometer reads X = 3.00 (dimensionless scale units), what is the sample temperature in kelvin?