# Chapter 13: Heat

**At Grade**Created by: CK-12

We know that heat rises from a hot object. This chapter studies the details of how heat moves between objects, based on their temperature and other properties. Topics will include temperature, kinetic theory of temperature, heat energy, and heat transfer via conduction, convection, and radiation.

### Chapter Summary

1. The conversion from temperature expressed in Celsius to kelvin is

\begin{align*}T_K=T_C \left(1 \frac{K}{C}\right)+273^\circ K\end{align*} or more simply \begin{align*}\rightarrow T_K=T_C+273\end{align*}

2. The relationship between the average kinetic energy of a gas and its temperature is \begin{align*}\overline{K} \overline{E}=\frac{1}{2} m(\overline{v}_t)^2=\frac{3}{2}kT\end{align*}, where \begin{align*}\overline{v}_t\end{align*} is the mean translational velocity of the molecules, \begin{align*}m\end{align*} is their mass, \begin{align*}k\end{align*} the Boltzmann constant, is equal to \begin{align*}1.38 \times 10^{-23} \frac{J}{K}\end{align*} and \begin{align*}T\end{align*} the temperature is expressed in Kelvin.

3. The internal energy can be directly related to the temperature of a gas as \begin{align*}U=N \left(\frac{3}{2} kT\right) \rightarrow U=\frac{3}{2} NkT\end{align*}

4. Energy that is transferred from one object to another object due to a temperature difference between the objects is called heat.

5. The amount of energy required to raise the temperature of one gram of water by one degree Celsius is defined as one *calorie*, or, as it is sometimes referred to, one “small” calorie. The calorie is therefore a measure of energy and it is equal to about 4.186 J.

Definition: \begin{align*}1000 \ small \ calories=1 \ food \ calorie=4186J \rightarrow 1.00kcal = 1.00kC=4186J\end{align*}

6. Energy can be transferred in three ways: through *conduction, convection,* and *radiation*.

a. Conduction occurs when a temperature difference exists causing the molecules of an object to transmit energy throughout the object.

b. Convection typically arises from the movement of gases or liquids over large distances.

c. Radiation is energy transferred by electromagnetic waves (or photons).

7. The relationship between the rate of heat flow (heat conduction) \begin{align*}\frac{\Delta E}{\Delta t}\end{align*} and the temperature difference \begin{align*}\Delta T\end{align*} is \begin{align*}\frac{\Delta E}{\Delta t}=kA \frac{\Delta T}{t}\end{align*}. Where, the rate of heat flow \begin{align*}\frac{\Delta E}{\Delta t}\end{align*}, is measured in \begin{align*}\frac{J}{s}, k\end{align*} is the thermal conductivity that depends upon the properties of the object, \begin{align*}A\end{align*} is the cross-section of the object, and \begin{align*}t\end{align*} is distance over which the heat is conducted between the two temperatures \begin{align*}\Delta T=T_2-T_1\end{align*}.

8. The specific heat \begin{align*}c\end{align*} of a material is the amount of energy needed to raise the temperature of one kilogram of a particular substance, one-degree Celsius.

The change in temperature \begin{align*}\Delta T\end{align*} of an object depends upon the amount of mass \begin{align*}m\end{align*} of the object being heated, the specific heat \begin{align*}c\end{align*} of the material the object is composed of and the amount of energy \begin{align*}\Delta Q\end{align*} transferred to the object. It can be experimentally shown that \begin{align*}\Delta T=\frac{\Delta Q}{mc} \rightarrow \Delta Q=mc \Delta T\end{align*}

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