Thermal Physics and Kinetic Theory

The Nature of Heat

For most of the 18th century, scientists believed heat was an invisible, massless fluid called caloric. On this view, an object heated up when caloric flowed into it and cooled when caloric flowed out.

Two experiments demolished the caloric model.

Rumford's Cannon-Boring Experiment

Benjamin Thompson (Count Rumford) observed that boring a brass cannon produced enormous amounts of heat, enough to boil water, and the heat continued as long as the boring continued. Under the caloric model, the caloric should have been exhausted. He also showed that the brass chips produced during boring had the same heat content as an equal mass of unbored brass, refuting the idea that caloric was being "squeezed out." He concluded that heat was generated by mechanical friction, not extracted from a finite store of fluid.

Joule's Paddle Wheel Experiment

In 1843, James Prescott Joule dropped a measured mass through a measured height, causing paddles to churn water. The work done ($W = mgh$) produced a temperature rise in the water. Joule showed that a fixed amount of work always produced the same amount of heat:

$4.2 \text{J} \equiv 1 \text{cal}$

This mechanical equivalent of heat proved that heat is a form of energy, not a substance. The caloric theory was abandoned in favour of the kinetic (energy transfer) theory of heat.

The Kinetic Theory of Heat

In the kinetic model:

• All matter is made of tiny particles (atoms and molecules) in constant random motion.
• Temperature is a measure of the average kinetic energy of these particles. Higher temperature means faster-moving particles.
• Heat is the net transfer of internal energy from a hotter body to a cooler body. Heat and temperature are not the same quantity.

Phases of Matter

Matter exists in three phases. Their properties are explained by the kinetic model.

When a solid is heated, particles gain enough energy to break free of their lattice positions and the substance melts (solid to liquid). Further heating gives particles enough energy to escape the liquid surface entirely and the substance boils or vaporises (liquid to gas). Both changes happen at fixed temperatures for a pure substance at a given pressure.

Temperature and Thermometers

Temperature is measured by finding a physical property of a substance that changes in a known, reproducible way with hotness. Common properties used include: volume of a liquid (liquid-in-glass thermometer), electrical resistance, and pressure of a gas at constant volume.

Fixed Points on the Celsius Scale

Two reference temperatures define the Celsius scale:

The interval between the two fixed points is divided into 100 equal divisions, so each division is one degree Celsius (°C).

Thermometer Types

Kelvin Scale

The Kelvin (absolute) scale uses the same size divisions as the Celsius scale but sets its zero at absolute zero, the temperature at which particles have minimum possible kinetic energy and all gas pressure would cease.

$T(\text{K}) = \theta(°\text{C}) + 273$

$\theta(°\text{C}) = T(\text{K}) - 273$

At absolute zero (0 K = −273 °C), molecular motion is at a minimum. Temperature in kelvin is always positive. Gas law calculations must use kelvin.

Thermal Expansion

Most substances expand when heated because their particles gain kinetic energy and push further apart. The amount of expansion depends on the phase:

• Solids expand least, particles vibrate about fixed positions and cannot move far.
• Liquids expand more than solids, particles can slide past each other.
• Gases expand most, particles are far apart and free to move; pressure drives them further apart.

Applications and Consequences of Thermal Expansion

A bimetallic strip bends toward the metal that expands less when heated (because the metal that expands more is on the outer, longer side of the curve).

FLASHCARD SET • 7 CARDSThermal Physics and Kinetic Theory: Quick Recall