Temperature vs Heat and Thermal Energy
Temperature is a measure of the average kinetic energy of the particles in a substance, thermal energy is the total kinetic energy of all the particles, and heat is the thermal energy that flows from a hotter to a colder object. In brief: a cup and a bathtub of water at 60 °C have the same temperature, but the bathtub holds far more thermal energy, and it takes far more heat to cool it down.
The three terms are used interchangeably in everyday speech, but in science they mean different things, and mixing them up is a common source of errors. This article defines each of them, compares them, explains the temperature scales with a conversion table and shows how to calculate the final temperature when objects at different temperatures are brought into contact.
How do temperature, thermal energy and heat differ?
Temperature is an intensive property: it does not depend on the amount of substance. For an ideal gas, the average translational kinetic energy per molecule is (3/2)kBT, where kB is the Boltzmann constant, 1.381 × 10−23 J/K. If you double the absolute temperature, you double the average kinetic energy of the particles.
Thermal energy is an extensive property: it depends on the number of particles as well as on their average energy. A large pot of water at 50 °C contains more thermal energy than a small cup of water at 90 °C, although the cup has a higher temperature.
Heat is energy in transit. It is not something an object has; it is the amount of thermal energy that is transferred between objects because of a difference in temperature. It flows spontaneously from a higher to a lower temperature, by conduction, convection or radiation.
Side-by-side comparison
| Property | Temperature | Thermal energy | Heat |
|---|---|---|---|
| What it measures | Average kinetic energy of particles | Total kinetic energy of particles | Energy transferred due to a temperature difference |
| Depends on amount? | No | Yes | Yes |
| Unit | K, °C, °F | J | J |
| Measured with | Thermometer | Calculated | Calorimeter |
What are the temperature scales?
- Kelvin (K): the SI scale, with 0 K at absolute zero, the lowest possible temperature. One kelvin is the same size as one degree Celsius.
- Celsius (°C): historically based on the freezing and boiling points of water at 1 atm, at 0 °C and 100 °C. K = °C + 273.15.
- Fahrenheit (°F): used in the United States. °F = 1.8 × °C + 32, and °C = (°F − 32) / 1.8.
Reference temperatures
| Reference point | Kelvin (K) | Celsius (°C) | Fahrenheit (°F) |
|---|---|---|---|
| Absolute zero | 0 | −273.15 | −459.67 |
| Water freezes (1 atm) | 273.15 | 0 | 32 |
| Room temperature | 293.15 | 20 | 68 |
| Human body (normal) | 310.15 | 37 | 98.6 |
| Water boils (1 atm) | 373.15 | 100 | 212 |
Since 2019 the kelvin is defined by fixing the value of the Boltzmann constant, and the Celsius scale is defined from the kelvin scale. Water at 1 atm actually boils at about 99.97 °C, so “100 °C” is a convenient approximation.
What happens when objects touch?
Heat flows from the hotter to the colder object until they have the same temperature, when they are in thermal equilibrium. This is the content of the zeroth law of thermodynamics: if A and B are each in equilibrium with C, then A and B are in equilibrium with each other, which makes it possible to define temperature and use thermometers. If no energy is lost to the surroundings, the heat lost by the hotter object equals the heat gained by the colder one: qhot = −qcold.
Worked examples
Example 1: converting temperatures
Convert 25 °C to kelvins and to °F. K = 25 + 273.15 = 298.15 K. °F = 1.8 × 25 + 32 = 77 °F. Convert 104 °F to °C: (104 − 32) / 1.8 = 40 °C.
Example 2: cup versus bathtub
How much heat is released when 200 g of water and 200 kg of water cool from 60 °C to 20 °C? The specific heat of water is 4.184 J/(g·°C). For the cup, q = 200 × 4.184 × 40 = 33,472 J, or 33.5 kJ. For the bathtub, the amount is a thousand times larger: 33,472 kJ. The temperature change is the same, but the heat is different because the amounts are different.
Example 3: mixing water
100 g of water at 80 °C is mixed with 200 g of water at 20 °C in an insulated container. What is the final temperature? Let T be the final temperature. Since the specific heat is the same, 100 × (80 − T) = 200 × (T − 20). This gives 8000 − 100T = 200T − 4000, so 300T = 12,000 and T = 40 °C. The result is a weighted average, closer to the temperature of the larger quantity of water.
Example 4: average kinetic energy of molecules
The average translational kinetic energy per molecule of any ideal gas at 300 K is (3/2)(1.381 × 10−23 J/K)(300 K) = 6.21 × 10−21 J. This is the same for helium and for chlorine, although helium atoms move much faster because they are lighter.
How did the ideas develop?
In the 1760s Joseph Black distinguished between the quantity of heat and the intensity of heat (temperature), through his studies on specific heat and latent heat. Daniel Fahrenheit introduced his scale in 1724 and Anders Celsius his in 1742 (originally with the boiling point as 0 and the freezing point as 100, later inverted). William Thomson (Lord Kelvin) proposed an absolute scale in 1848. The kinetic theory in the second half of the 19th century explained temperature as molecular motion, and the Boltzmann constant provided the link between the molecular and macroscopic scales.
Which mistakes are common?
- Saying that “cold” flows: only heat flows, from hot to cold.
- Calling temperature “heat”: temperature is not an amount of energy.
- Assuming that a higher temperature always means more thermal energy: the amount of substance also matters.
- Adding 273 to a Fahrenheit value: Fahrenheit needs a different conversion.
- Averaging temperatures without weighting: mix by mass and specific heat.