Heat, Temperature, And Thermal Equilibrium

Touch a warm mug to a cool metal spoon and both change. Something has passed between them, and the passing stops only when nothing more tends to change. Thermodynamics begins by naming what is passing, what is being measured, and what it means for a system to be done changing.

Thermal contact and thermal equilibrium

Two objects are in thermal contact when energy can move between them because of a temperature difference, for example by conduction through a shared surface. When that exchange has run its course, the objects reach thermal equilibrium. Thermal equilibrium means their measurable thermal state stops drifting in time when left undisturbed, and no net energy transfer occurs between them due to temperature difference.

A thermometer is a third system that is allowed to come into thermal contact with something else. The key assumption is that the thermometer is small enough, or coupled weakly enough, that it does not significantly change the final equilibrium state it is trying to measure.

The zeroth law of thermodynamics turns that physical idea into a consistency rule for temperature measurement.

If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other.

This law does not compute a number. It guarantees that temperature is a property you can assign to a system so that equal temperature corresponds to thermal equilibrium.

Use the annotated scenario to track which bodies exchange energy, what stops changing at equilibrium, and why the thermometer can serve as the middle system C.

If A and B both settle to the same thermometer reading, the zeroth law says they share a common temperature, even if A and B never touched.

Heat versus internal energy

Heat $Q$ is energy in transit across a system boundary due only to a temperature difference. Its SI unit is the joule, $\text{J}$. Heat is not something an object contains. It is something that happens during a process.

Internal energy $U$ is energy stored in the microscopic degrees of freedom of a system, such as molecular translation, rotation, vibration, and interactions. Its SI unit is also $\text{J}$. Unlike heat, internal energy is a state property. For a system in equilibrium, $U$ depends on the state, not on the path taken to reach it.

A quick way to keep the categories straight is to ask a grammar question. Heat is a verb in physics. Internal energy is a noun.

When two bodies at different temperatures are placed in thermal contact and isolated from everything else, energy transfers as heat from the higher temperature body to the lower temperature body until they reach a common final temperature. During that process, each body’s internal energy changes. The heat is the transfer mechanism across the boundary, and the internal energy change is what happened to each body.

The next interaction lets you vary mass, material, and initial temperatures to separate two ideas that beginners often fuse. How much heat flows depends on the details, while the final equilibrium temperature depends on energy balance and thermal properties.