Temperature
Temperature is a measure related to the thermal state of a system. At the microscopic level, the particles of matter are constantly moving, and their thermal behaviour is connected to the energy associated with that motion.
Temperature is not the same thing as total thermal energy. A large object and a small object can have the same temperature while containing different amounts of thermal energy.
Heat and thermal energy
Heat is energy transferred between systems because of a temperature difference. Energy naturally transfers from a region of higher temperature toward a region of lower temperature until thermal equilibrium is approached.
Specific heat capacity
Different materials require different amounts of energy to produce the same temperature change. Specific heat capacity describes this property.
Q = mcΔT
Q is transferred thermal energy, m is mass, c is specific heat capacity, and ΔT is the temperature change.
Changes of state
Matter can change between solid, liquid, and gaseous states. During a phase change, energy can be transferred without producing the same kind of temperature increase that occurs when the substance remains in one phase.
Q = mL
L is the specific latent heat associated with the particular change of state.
Thermal expansion
Heating a substance generally changes the average separation between its particles. As a result, many materials expand when their temperature increases.
For a simple uniform rod, the change in length can be approximated using the coefficient of linear expansion.
ΔL = αL₀ΔT
α is the coefficient of linear expansion and L₀ is the original length.
Gas laws
Gases are strongly affected by pressure, volume, and temperature. Several simple relationships can be combined into the ideal gas law.
PV = nRT
P is pressure, V is volume, n is amount of substance, R is the gas constant, and T is absolute temperature.
Internal energy
The internal energy of a system is associated with the microscopic kinetic and potential energies of its particles.
A system's internal energy can change when energy is transferred as heat or when work is done on or by the system.
ΔU = Q − W
With this convention, W represents work done by the system. Sign conventions should always be stated when using thermodynamic equations.
Thermal equilibrium
When two systems are allowed to exchange thermal energy and eventually reach the same temperature, they are said to be in thermal equilibrium.
This idea forms the basis of temperature measurement and connects naturally to the zeroth law of thermodynamics.
Quick example
A 2 kg sample has a specific heat capacity of 500 J/(kg·K). How much energy is required to increase its temperature by 10 K?
Using:
Q = mcΔT
Q = 2 × 500 × 10