Heat vs Temperature and Thermal Equilibrium
Temperature is a measure of the average kinetic energy of the particles in a substance, while heat is the energy transferred between objects because of a temperature difference; thermal equilibrium is reached when two objects in contact have the same temperature and no net heat flows. In brief: heat flows spontaneously from a hotter object to a colder one. Temperature is measured in degrees Celsius or kelvins, and heat in joules. A large cool object can hold more thermal energy than a small hot one.
In everyday speech, “heat” and “temperature” are used interchangeably, but in physics they are different. This guide defines temperature, thermal energy and heat, explains thermal equilibrium and the zeroth law, compares the quantities in a table, works through a mixing problem and corrects common mistakes.
What is temperature?
Temperature tells how hot or cold an object is relative to a standard. On the microscopic level, it is proportional to the average random kinetic energy of the particles: the faster they move, the higher the temperature. It does not depend on the number of particles. A cup of tea and a bath of tea at 60 °C have the same temperature. Temperature is measured with thermometers, which use a property that changes regularly with temperature, such as the expansion of a liquid or the resistance of a thermistor.
What is heat?
The internal (thermal) energy of an object is the sum of the kinetic and potential energies of all its particles. Heat is the energy that moves from one object to another because of a difference in temperature, by conduction, convection or radiation. Heat is a process of transfer, and it is measured in joules. Objects do not “contain” heat: they contain internal energy. When an object gains energy by heating, its particles move faster (the temperature rises) or the arrangement changes (change of state).
What is thermal equilibrium?
When two objects at different temperatures are in contact, energy flows from the hotter to the colder, until both have the same temperature. At that point they are in thermal equilibrium, and there is no net flow of energy. The zeroth law of thermodynamics says that if A is in thermal equilibrium with B, and B with C, then A is in thermal equilibrium with C. This is the basis for the use of thermometers: a thermometer in equilibrium with an object shows the object’s temperature.
Temperature, thermal energy and heat compared
| Quantity | What it measures | Unit | Depends on the amount of substance? |
|---|---|---|---|
| Temperature | Average kinetic energy of particles | °C, K | No |
| Internal energy | Total energy of the particles | J | Yes |
| Heat | Energy transferred due to temperature difference | J | Yes |
Worked example: mixing water
2.0 kg of water at 80 °C is mixed with 1.0 kg of water at 20 °C in an insulated container. Find the final temperature.
- Energy balance: the heat lost by the hot water equals the heat gained by the cold water. Both have the same specific heat capacity c, so it cancels.
- Equation: 2.0 × c × (80 − T) = 1.0 × c × (T − 20).
- Solve: 160 − 2T = T − 20, so 180 = 3T and T = 60 °C. As a check, this is the weighted average (2.0 × 80 + 1.0 × 20) ÷ 3.0 = 180 ÷ 3.0 = 60 °C.
- Heat transferred: Q = 1.0 × 4,180 × (60 − 20) = 167,200 J. The hot water lost the same energy: 2.0 × 4,180 × 20 = 167,200 J.
Note that the temperature is closer to that of the hot water because there is more of it. A bath of water at 40 °C stores much more internal energy than a cup of water at 90 °C, although its temperature is lower.
How were heat and temperature understood?
In the 1700s heat was thought to be a fluid called caloric. Count Rumford’s cannon-boring experiments (1798) showed that mechanical work could produce heat without limit, and James Joule showed in the 1840s that heat is a form of energy. The kinetic theory in the 19th century linked temperature to the motion of particles. Joseph Black distinguished heat from temperature in the 1760s, and Ralph Fowler formulated the zeroth law in the 1930s.
Which mistakes are common?
Mistake 1: Using heat and temperature as the same quantity
Temperature measures how hot, heat is energy in transfer.
Mistake 2: Saying that cold flows into a warm object
Only heat flows, from hot to cold. “Cold” is the absence of heat.
Mistake 3: Thinking that objects at the same temperature have the same energy
Internal energy depends on the mass and the material as well.
Mistake 4: Believing that the thermometer shows its own temperature of the object before equilibrium
A thermometer shows its own temperature, which equals that of the object only when they are in equilibrium.