6. Temperature and heat

$$ \Delta L = \alpha L \Delta T $$

$$ \Delta V = \beta V \Delta T $$

$$ \beta = 3\alpha $$

$\alpha$ is coefficient of linear expansion, $\beta$ coefficient of volume expansion.

$$ dQ = mc dT $$

Specific heat or specific heat capacity or just heat capacity

$$ c = \frac{1}{m}\frac{dQ}{dT} $$

Calorimetry:

$$ Q = mc \Delta T $$

$$ Q_c + Q_h = 0 $$

For fusion: $$ Q = m L_f $$

For evaporation: $$ Q = m L_v $$

$L_f$ is heat of fusion and $L_v$ heat of vaporization.

Rate of conductive heat transfer

$$ P = \frac{dQ}{dT} = -kA \frac{dT}{dx} $$

where $k$ is the thermal conductivity.

The rate of radiated heat transfer

$$ P = \sigma A e T^4 $$

where $\sigma$ is the Stefan-Boltzmann constant and $e$ the emissivity. If there is a surrounding,

$$ P_{net} = \sigma A e (T_2^4-T_1^4) $$

$$ pV = nRT = Nk_BT $$

$$ p = \rho k_BT $$

Average kinetic energy of a molecule in a gas

$$ K = \frac{1}{2} mv^2 = \frac{3}{2} k_B T $$

Total internal energy of the gas

$$ E_{int} = NK = \frac{3}{2} Nk_BT = \frac{3}{2} nRT $$

RMS speed of a molecule

$$ v_{rms} = \sqrt{v^2} = \sqrt{\frac{3k_BT}{m}} $$