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Heat and temperature
Heat is a form of energy.
Temperature is a measure of internal motion of atoms and molecules.
Zeroth Law of Thermodynamics:
if
$$A {\stackrel{\mbox{eq-m}}{\longleftrightarrow}} B \quad \mbox{ and } \quad
B {\stackrel{\mbox{eq-m}}{\longleftrightarrow}} C$$
then
$$A {\stackrel{\mbox{eq-m}}{\longleftrightarrow}} C$$
Temperature scales: Celsius (\(T_C\)), Fahrenheit (\(T_F\)), Kelvin (absolute, \(T\))
$$
\begin{eqnarray*}
T_F & = & \frac{9}{5} \frac{^\circ \mbox{F}}{^\circ \mbox{C}} T_C + 32^\circ \mbox{F} \\
T_C & = & \frac{5}{9} \frac{^\circ \mbox{C}}{^\circ \mbox{F}} ( T_F - 32^\circ \mbox{F}) \\
T & = & T_C + 273.15
\end{eqnarray*}
$$
Thermal expansion:
$$
\begin{eqnarray*}
\mbox{length (1D):} & & \Delta L = \alpha L_0 \Delta T\\
\mbox{area (2D):} & & \Delta A = 2 \alpha A_0 \Delta T\\
\mbox{volume (3D):} & & \Delta V = 3 \alpha V_0 \Delta T = \beta V_0 \Delta T
\end{eqnarray*}
$$
Heat capacity:
$$
C=\frac{Q}{\Delta T} , \quad [C] =\frac{\mbox{J}}{\mbox{K}}
$$
Specific heat:
$$
c=\frac{Q}{m \Delta T} , \quad [c] = \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}
$$
For example, \(c_{\mbox{water}} = 4186 \frac{\mbox{J}}{\mbox{kg}\cdot\mbox{K}} = 1 \frac{\mbox{kcal}}{\mbox{kg}\cdot\mbox{K}}\), where
1 cal = 4.186 J
Latent heat: \(Q = m L_f\) for fusion (melting) or
\(Q = m L_v\) for vaporization
Heat conduction:
$$
\frac{\displaystyle \Delta Q}{\displaystyle \Delta t} = k_B A \frac{\displaystyle \Delta T}{\displaystyle L}
$$
Radiation:
$$
\frac{\displaystyle \Delta Q}{\displaystyle \Delta t} =
e \sigma A \left(T^4 - T_{\rm surround}^4\right)
$$
with
Stefan-Boltzmann constant $$\sigma=5.67\times 10^{-8} \frac{\mbox{W}}{\mbox{m}^2\mbox{K}^4}$$
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