## 14.1 Heat

- Heat and work are the two distinct methods of energy transfer.
- Heat is energy transferred solely due to a temperature difference.
- Any energy unit can be used for heat transfer, and the most common are kilocalorie (kcal) and joule (J).
- Kilocalorie is defined to be the energy needed to change the temperature of 1.00 kg of water between $\text{14}\text{.}\mathrm{5\xbaC}$ and $\text{15}\text{.}\mathrm{5\xbaC}$.
- The mechanical equivalent of this heat transfer is $1\text{.00 kcal}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}\text{4186 J.}$

## 14.2 Temperature Change and Heat Capacity

- The transfer of heat $Q$ that leads to a change $\text{\Delta}T$ in the temperature of a body with mass $m$ is $Q=\text{mc}\text{\Delta}T$, where $c$ is the specific heat of the material. This relationship can also be considered as the definition of specific heat.

## 14.3 Phase Change and Latent Heat

- Most substances can exist either in solid, liquid, and gas forms, which are referred to as “phases.”
- Phase changes occur at fixed temperatures for a given substance at a given pressure, and these temperatures are called boiling and freezing (or melting) points.
- During phase changes, heat absorbed or released is given by:
$$Q=\text{mL,}$$
where $L$ is the latent heat coefficient.

## 14.4 Heat Transfer Methods

- Heat is transferred by three different methods: conduction, convection, and radiation.

## 14.5 Conduction

- Heat conduction is the transfer of heat between two objects in direct contact with each other.
- The rate of heat transfer $Q/t$ (energy per unit time) is proportional to the temperature difference ${T}_{2}-{T}_{1}$ and the contact area $A$ and inversely proportional to the distance $d$ between the objects:
$$\frac{Q}{t}=\frac{\text{kA}\left({T}_{2}-{T}_{1}\right)}{d}\text{.}$$

## 14.6 Convection

- Convection is heat transfer by the macroscopic movement of mass. Convection can be natural or forced and generally transfers thermal energy faster than conduction. Table 14.4 gives wind-chill factors, indicating that moving air has the same chilling effect of much colder stationary air.
*Convection that occurs along with a phase change*can transfer energy from cold regions to warm ones.

## 14.7 Radiation

- Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.
- The rate of heat transfer depends on the surface area and the fourth power of the absolute temperature:
$$\frac{Q}{t}=\sigma eA{T}^{4}\text{,}$$
where $\sigma =5\text{.67}\times {\text{10}}^{-8}\phantom{\rule{0.25em}{0ex}}\text{J/s}\cdot {\text{m}}^{2}\cdot {\text{K}}^{4}$ is the Stefan-Boltzmann constant and $e$ is the emissivity of the body. For a black body, $e=1$ whereas a shiny white or perfect reflector has $e=0$, with real objects having values of $e$ between 1 and 0. The net rate of heat transfer 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 an object surrounded by an environment with uniform temperature ${T}_{2}$ and $e$ is the emissivity of the

*object*.