13.1 Temperature

Temperature and thermal energy describe how hot or cold objects are and the energy associated with the motion of their particles. These concepts form the foundation for understanding heat transfer and thermodynamics, which come up throughout the rest of this unit.

Temperature and Thermal Energy

Temperature and thermal energy

Temperature measures the average kinetic energy of particles in a substance. When particles move faster on average, the temperature is higher. Boiling water has particles zipping around with high average kinetic energy, while the particles in an ice cube move much more slowly.

Thermal energy is the total kinetic energy of all particles in a substance. This depends on both temperature and the amount of matter present. A cup of coffee and a full pot of coffee might be at the same temperature, but the pot has far more thermal energy because it contains more particles. Similarly, an ice cube and an iceberg can both sit at 0°C, yet the iceberg holds vastly more thermal energy due to its enormous mass.

The distinction matters: temperature tells you about the average energy per particle, while thermal energy tells you about the total energy in the whole object.

• Heat capacity is the amount of heat required to raise the temperature of an object by one degree
• Specific heat is heat capacity per unit mass, which lets you compare different materials directly (water has a high specific heat of $4{,}186 \, \text{J/(kg·°C)}$, meaning it takes a lot of energy to change its temperature)

Conversion of temperature scales

Three temperature scales show up regularly in physics:

• Celsius (°C) and Fahrenheit (°F) are relative scales, meaning their zero points are chosen based on convenient reference points (the freezing point of water for Celsius, for example).
• Kelvin (K) is an absolute scale. Its zero point, called absolute zero (0 K = −273.15°C), is the lowest temperature physically possible. At absolute zero, particle motion reaches its minimum. Kelvin is the standard unit in most physics equations.

Celsius ↔ Fahrenheit:

$°F = °C \times \frac{9}{5} + 32$

$°C = (°F - 32) \times \frac{5}{9}$

Celsius ↔ Kelvin:

$K = °C + 273.15$

$°C = K - 273.15$

Fahrenheit ↔ Kelvin:

$K = (°F - 32) \times \frac{5}{9} + 273.15$

$°F = (K - 273.15) \times \frac{9}{5} + 32$

A quick example: Room temperature is about 20°C. In Kelvin, that's $20 + 273.15 = 293.15 \, \text{K}$. In Fahrenheit, that's $20 \times \frac{9}{5} + 32 = 68°\text{F}$.

Thermal Equilibrium and the Zeroth Law of Thermodynamics

Thermal equilibrium in heat transfer

Thermal equilibrium is the state where two or more systems in thermal contact share the same temperature. Once they reach equilibrium, no net heat transfer occurs between them. A cup of coffee left on a counter eventually reaches room temperature and stops exchanging heat with the surrounding air.

Heat always flows from the higher-temperature system to the lower-temperature one. The temperature difference between two objects is what drives heat transfer. Drop an ice cube into warm water, and heat flows from the water into the ice until both reach the same final temperature.

Zeroth law of thermodynamics

The Zeroth Law states: if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other. This might sound obvious, but it's what makes temperature measurement possible in the first place. Without it, you couldn't trust that a thermometer reading tells you anything meaningful about two different objects.

Practical applications of the Zeroth Law:

1. Thermometers rely on the Zeroth Law directly. When a thermometer reaches thermal equilibrium with your body, its reading reflects your body's temperature. Calibration uses fixed reference points like the freezing point (0°C) and boiling point (100°C) of water at standard pressure.
2. Thermostats use temperature sensors that reach equilibrium with the surrounding environment, then trigger heating or cooling systems to maintain a set temperature in ovens, refrigerators, and HVAC systems.
3. Thermal insulation works by slowing down the process of reaching thermal equilibrium. Materials like fiberglass and foam resist heat flow, keeping the temperature difference between two sides for longer.

Thermal effects

• Thermal expansion occurs when materials increase in size as temperature rises. The particles vibrate more and push slightly farther apart, causing the material to expand.
• Latent heat is the energy absorbed or released during a phase change (like melting or boiling) without any change in temperature. All the energy goes into breaking or forming bonds between particles rather than speeding them up.