### Summary

- Temperature is operationally defined as the quantity measured by a thermometer. It is proportional to the average kinetic energy of atoms and molecules in a system.
- Thermal equilibrium occurs when two bodies can freely exchange energy but no net energy is transferred between them.
- The zeroth law of thermodynamics states that when two systems,
*A*and*B,*are in thermal equilibrium with each other, and*B*is in thermal equilibrium with a third system*C*, then*A*is also in thermal equilibrium with*C*.

- Three types of thermometers are alcohol, liquid crystal, and infrared radiation (pyrometer).
- The three main temperature scales are Celsius, Fahrenheit, and Kelvin. Temperatures can be converted from one scale to another using temperature conversion equations.
- The three phases of water (ice, liquid water, and water vapor) can coexist at a single pressure and temperature known as the triple point.

- Thermal expansion is the increase of the size (length, area, or volume) of a body due to a change in temperature, usually a rise. Thermal contraction is the decrease in size due to a change in temperature, usually a fall in temperature.
- Thermal stress is created when thermal expansion or contraction is constrained.

- Heat and work are the two distinct methods of energy transfer.
- Heat transfer to an object when its temperature changes is often approximated well by $Q=mc\text{\Delta}T,$ where
*m*is the object’s mass and*c*is the specific heat of the substance.

- Most substances have three distinct phases (under ordinary conditions on Earth), and they depend on temperature and pressure.
- Two phases coexist (i.e., they are in thermal equilibrium) at a set of pressures and temperatures.
- Phase changes occur at fixed temperatures for a given substance at a given pressure, and these temperatures are called boiling, freezing (or melting), and sublimation points.

- Heat is transferred by three different methods: conduction, convection, and radiation.
- Heat conduction is the transfer of heat between two objects in direct contact with each other.
- The rate of heat transfer
*P*(energy per unit time) is proportional to the temperature difference via conduction through a slab of material with ends in contact with two objects at different temperatures ${T}_{h}$ and ${T}_{c}$ is proportional to the temperature difference ${T}_{h}\phantom{\rule{0.2em}{0ex}}\u2013\phantom{\rule{0.2em}{0ex}}{T}_{c}$ and the contact area*A*, and inversely proportional to the distance*d*between the ends. - Convection is heat transfer by the macroscopic movement of mass. Convection can be natural or forced, and generally transfers thermal energy faster than conduction.
- Radiation is heat transfer through the emission or absorption of electromagnetic waves.
- The rate of radiative heat transfer is proportional to the emissivity
*e*. For a perfect blackbody, $e=1$, whereas a perfectly white, clear, or reflective body has $e=0$, with real objects having values of*e*between 1 and 0. - The rate of heat emission depends on the surface area and the fourth power of the absolute temperature:
$$P=\sigma eA{T}^{4},$$where $\sigma =5.67\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{J/s}\xb7{\text{m}}^{2}\xb7{\text{K}}^{4}$ is the Stefan-Boltzmann constant and
*e*is the emissivity of the body. The net rate of heat transfer from an object by radiation is$$\frac{{Q}_{\text{net}}}{t}=\sigma eA\left({T}_{2}{}^{4}-{T}_{1}{}^{4}\right),$$where ${T}_{1}$ is the temperature of the object surrounded by an environment with uniform temperature ${T}_{2}$ and*e*is the emissivity of the object.