In everyday language, "heat" and "temperature" are often used interchangeably. In physics, they have very precise and distinct meanings.

Most materials expand when heated and contract when cooled. For solids and liquids, this expansion is typically proportional to the temperature change.

The amount of heat ($Q$) required to change the temperature of a substance depends on its mass ($m$) and a material property called specific heat capacity.

When a substance undergoes a phase change (like melting or boiling), heat is added or removed without any change in temperature. The energy goes into breaking or forming intermolecular bonds.

There are three fundamental mechanisms by which heat is transferred:

• Conduction: Heat transfer through stationary matter by physical contact (e.g., a metal spoon getting hot in soup).
• Convection: Heat transfer by the macroscopic movement of a fluid (e.g., hot air rising, water circulating in a pot). Natural convection is driven by buoyant forces, while forced convection uses pumps or fans.
• Radiation: Heat transfer by electromagnetic waves (e.g., feeling the heat from the sun or a fire). Does not require a medium.

These four empirical laws govern all macroscopic interactions involving energy and temperature.

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

This law defines temperature: two systems in thermal equilibrium have the same temperature.

The First Law is the principle of conservation of energy applied to thermal systems. It states that the change in a system's internal energy ($\Delta U$) is equal to the net heat added to the system ($Q$) minus the net work done by the system on its surroundings ($W$).

The work done by a gas is equal to the area under the curve on a Pressure-Volume (P-V) diagram.

When a gas changes state (pressure, volume, temperature), it follows a specific process. The First Law applies to all of them, but simplifies uniquely for each:

• Isothermal Process (Constant Temperature): $\Delta T = 0$, so $\Delta U = 0$ (for an ideal gas). Therefore, $Q = W$. Heat added is entirely converted to work done by the gas.
• Isobaric Process (Constant Pressure): $W = P \Delta V$. Heat added changes both internal energy and does work.
• Isochoric (Isovolumetric) Process (Constant Volume): $\Delta V = 0$, so $W = 0$. Therefore, $\Delta U = Q$. All heat added goes into increasing the internal energy.
• Adiabatic Process (No Heat Transfer): $Q = 0$. Therefore, $\Delta U = -W$. If the gas expands and does work, its internal energy (and thus temperature) must decrease.

The First Law says energy is conserved, but it doesn't restrict the direction of energy transfer. The Second Law dictates that direction. There are several equivalent statements of the Second Law:

• Clausius Statement: Heat can never pass spontaneously from a colder body to a warmer body.
• Kelvin-Planck Statement: It is impossible to construct a heat engine that, operating in a cycle, extracts heat from a single reservoir and converts it entirely into work. Some heat must be expelled to a colder sink. (No engine is 100% efficient).
• Entropy Statement: The total entropy ($S$) of an isolated system can never decrease over time. $\Delta S_{total} \ge 0$.

A heat engine is a device that extracts heat ($Q_H$) from a hot reservoir, uses some of it to do useful work ($W$), and exhausts the remaining waste heat ($Q_C$) to a cold reservoir.

By the First Law, $W = Q_H - |Q_C|$.

The thermal efficiency ($e$) is the ratio of what you get to what you pay for:

The Carnot Engine is an idealized, reversible engine that sets the maximum possible theoretical efficiency between two temperatures:

It is impossible to lower the temperature of any system to absolute zero (0 K) in a finite number of steps. As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.

The Ideal Gas Law ($PV = nRT$) relates the macroscopic properties of a gas: pressure, volume, temperature, and amount of substance.

The Kinetic Theory of Gases provides the microscopic explanation for these macroscopic properties. It models a gas as a large number of tiny, rapidly moving particles in random, continuous motion, colliding elastically with each other and the container walls. The pressure exerted by a gas is the macroscopic result of billions of microscopic particle collisions against the container.