Chapter 11: Thermal Physics and Properties of Matter

Temperature and heat

Temperature measures how hot a body is; heat is energy transferred because of a temperature difference. The kelvin scale has . To change temperature, ( is the specific heat capacity); to change state, ( is the specific latent heat). Example: heating 2 kg of water () through 20 K needs J.

The ideal gas and kinetic theory

An ideal gas obeys , where and . Special cases: Boyle ( constant at constant ), Charles ( constant at constant ), and Gay-Lussac ( constant at constant ).

Kinetic theory explains pressure through molecular collisions: . The mean translational kinetic energy per molecule is , so temperature is a measure of molecular kinetic energy. The root-mean-square speed is . Example: for nitrogen () at 300 K, .

The laws of thermodynamics

Zeroth law: bodies in thermal equilibrium with a third are in equilibrium with each other (the basis of temperature).

First law: , where is heat added to the system and is work done by the system. Energy is conserved.

Second law: heat does not flow spontaneously from cold to hot; entropy of an isolated system does not decrease. No engine can convert heat entirely to work.

For a gas, an isothermal change has ; an adiabatic change () has with . A heat engine has efficiency , and the maximum efficiency (Carnot) between reservoirs and is . Example: between 600 K and 300 K, .

Heat transfer

Conduction: , with the thermal conductivity.

Convection: transfer by moving fluid.

Radiation: power radiated by a body (Stefan–Boltzmann, for a black body), and Wien’s law .

Elasticity

Stress , strain , Young modulus within the elastic limit (Hooke’s law). The strain energy stored is . Example: a wire 2 m long with cross-section under 100 N extends by 1 mm: Pa, , Pa.

Fluids

Pressure: ; in a fluid at depth , .

Archimedes’ principle: the upthrust equals the weight of fluid displaced.

Continuity (incompressible): . Bernoulli (steady, non-viscous): .

Viscosity: Stokes’ law for a small sphere; a falling sphere reaches terminal velocity when weight = upthrust + drag.

Surface tension: ; excess pressure inside a drop and a soap bubble ; capillary rise . Example: water () in a tube of radius 0.5 mm rises cm.

Common mistakes

Using Celsius in the gas laws. Always use kelvin.

Confusing the sign convention for work in the first law (work done on versus by the gas).

Forgetting to convert grams to kilograms in .

Practice questions

How much heat is needed to turn 0.5 kg of ice at 0 °C to water at 0 °C? () [ J]

A gas at 300 K and 100 kPa is heated at constant volume to 450 K. Find the new pressure. [150 kPa]

Find the maximum efficiency between 500 K and 300 K. [40%]