====== 6. Temperature and heat ====== ===== - Zeroth law of thermodynamics ===== {{ :courses:phy101:6.1.jpg?nolink&400 |}} ===== - Temperature ===== {{ :courses:phy101:6.2.jpg?nolink&600 |}} ===== - Thermal expansion ===== {{ :courses:phy101:6.3.jpg?nolink |}} $$ \Delta L = \alpha L \Delta T $$ $$ \Delta V = \beta V \Delta T $$ $$ \beta = 3\alpha $$ $\alpha$ is coefficient of linear expansion, $\beta$ coefficient of volume expansion. {{ :courses:phy101:6.4.jpg?nolink&500 |}} ===== - Heat ===== {{ :courses:phy101:6.5.jpg?nolink |}} {{ :courses:phy101:6.6.jpg?nolink&400 |}} ==== - Heat capacity ==== $$ dQ = mc dT $$ Specific heat or specific heat capacity or just heat capacity $$ c = \frac{1}{m}\frac{dQ}{dT} $$ Calorimetry: $$ Q = mc \Delta T $$ $$ Q_c + Q_h = 0 $$ ===== - Phase changes ===== {{ :courses:phy101:6.7.jpg?nolink&400 |}} For fusion: $$ Q = m L_f $$ For evaporation: $$ Q = m L_v $$ $L_f$ is heat of fusion and $L_v$ heat of vaporization. {{ :courses:phy101:6.8.jpg?nolink600 |}} {{ :courses:phy101:6.9.jpg?nolink |}} ===== - Heat transfer ===== {{ :courses:phy101:6.10.jpg?nolink&450 |}} ==== - Conduction ==== {{ :courses:phy101:6.11.jpg?nolink&500 |}} Rate of conductive heat transfer $$ P = \frac{dQ}{dT} = -kA \frac{dT}{dx} $$ where $k$ is the thermal conductivity. ==== - Convection ==== {{ :courses:phy101:6.12.jpg?nolink&400 |}} ==== - Radiation ==== {{ :courses:phy101:6.13.jpg?nolink&550 |}} 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, $$ P_{net} = \sigma A e (T_2^4-T_1^4) $$ {{ :courses:phy101:6.14.jpg?nolink&450 |}} ===== - Ideal gas ===== {{ :courses:phy101:6.15.jpg?nolink |}} $$ pV = nRT = Nk_BT $$ $$ p = \rho k_BT $$ ===== - Kinetic theory of gas ===== 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 $$ v_{rms} = \sqrt{v^2} = \sqrt{\frac{3k_BT}{m}} $$