Temperature and Heat

Overview

Temperature and Heat is now best read as a bridge note across Thermal Physics A and Thermal Physics B.

Temperature describes the thermal state of a body. Heat is energy transferred because of a temperature difference.

Definition

Temperature is a physical quantity that indicates how hot or cold a body is. At microscopic level, temperature is related to the average random kinetic energy of particles.

For thermodynamic temperature, use $T$ in kelvin. For Celsius temperature, use $\theta$ in ${}^{\circ }\text{C}$.

$$T=\theta +273.15$$

Heat is energy transferred from one body to another due to a temperature difference. It flows from higher temperature to lower temperature until thermal equilibrium is reached.

Heat is not a property stored inside a body. The energy stored microscopically in a body is internal energy.

Why It Matters

Many students lose marks by writing “heat inside the object”, “temperature flows”, or “heat increases when an object is bigger”. Correct language is that heat is transferred, temperature does not flow, and internal energy changes when heat is transferred or work is done.

This distinction is required in specific heat capacity, latent heat, the first law of thermodynamics, kinetic theory, and ideal gas processes.

Key Representations

Internal energy $U$ is the total microscopic energy of a system:

• random kinetic energy of particles;
• intermolecular potential energy.

When two bodies in thermal contact have no net heat transfer between them, they are in thermal equilibrium. They have the same temperature.

The zeroth law of thermodynamics states that if body A is in thermal equilibrium with B, and B with C, then A is in thermal equilibrium with C. This principle allows thermometers to work.

Temperature conversions:

$$0^{\circ }\text{C}=273.15\text{K}$$ $$100^{\circ }\text{C}=373.15\text{K}$$

When no change of state occurs:

$$Q=mc\Delta T$$

For an ideal gas:

$$⟨E_k⟩=\frac{3}{2}kT$$

Large heat capacity means a smaller temperature rise for the same thermal energy input:

$$\Delta T=\frac{Q}{C}$$

Common Exam Traps

Do not say heat is stored in an object. Say internal energy is stored and heat is transferred into or out of the object.

Do not say cold flows into a body. Heat flows out of the hotter body into the colder body.

Do not use Celsius temperature in proportional gas-law statements. Use kelvin for $V\propto T$ and $p\propto T$.

Same temperature does not mean same internal energy. A bucket of water and a cup of water can have the same temperature but different internal energies.

Temperature is an intensive property; it does not depend directly on amount of substance.

Links

• Thermal Physics A
• Thermal Physics B
• Thermal Measurement and Scales
• Heat Capacity and Latent Heat
• Kinetic Theory and Ideal Gases
• First Law and Thermodynamic Processes
• Measurement