\begin{equation} T_K = T_C + 273.15 \qquad \textnormal{(Celsius to kelvin)} \end{equation} \begin{equation} T_{F} = \frac{9}{5} \, T_C + 32 \qquad \textnormal{(Celsius to fahrenheit)} \end{equation} \begin{equation} T_{C} = \frac{5}{9} (T_F - 32) \qquad \textnormal{(Fahrenheit to celsius)} \end{equation} \begin{equation} \frac{T_2}{T_1} = \frac{p_2}{p_1} \qquad \textnormal{(Ratio between temperature and gas thermometer pressure)} \end{equation}
\begin{equation} \Delta L = \epsilon L_0 \Delta T \qquad \textnormal{(Change in length, T = temperature)} \end{equation} \begin{equation} \Delta V = \sigma V_0 \Delta T \qquad \textnormal{(Change in volume)} \end{equation} \begin{equation} \mu = \frac{F}{A} = - Y \epsilon \Delta T \qquad \textnormal{(Tensile stress)} \end{equation}
\begin{equation} Q = m \, c \, \Delta T \qquad \textnormal{(Heat exchange, c = specific heat capacity)} \end{equation} \begin{equation} Q = N \, C \, \Delta T \qquad \textnormal{(Heat exchange, C = molar heat capacity)} \end{equation} \begin{equation} Q = \pm \, m \, L \qquad \textnormal{(Heat exchange, L = heat phase constant)} \end{equation}
\begin{equation} \tau = \frac{dQ}{dt} = k A \frac{T_H - T_C}{L} \qquad \textnormal{(Heat current, A = area, L = length)} \end{equation} \begin{equation} \tau = A \, e \, \sigma T^4 \qquad \textnormal{(Heat current, e = emissivity)} \end{equation} \begin{equation} \tau_{net} = A \, e \, \sigma (T^4 - T_s^4 ) \qquad \textnormal{(Heat current, \(T_s \) = surroundings)} \end{equation}
\begin{equation} W = \int_{V_1}^{V_2} p \, dV \qquad \textnormal{(Work through variable pressure)} \end{equation} \begin{equation} W = p \, (V_2 - V_1) \qquad \textnormal{(Work through constant pressure)} \end{equation}
\begin{equation} \Delta U = Q + W \qquad \textnormal{(First law of thermodynamics)} \end{equation} \begin{equation} dU = dQ + dW \qquad \textnormal{(Infinitesimal work)} \end{equation}
Isothermal: \( \Delta T = 0 \)
Isobaric: \( \Delta p = 0 \)
Isochoric: \( \Delta V = 0 \)
Adiabatic: \( Q = 0 \)
\begin{equation} C_p = C_v + R \qquad \textnormal{(Molar heat capacity at constant pressure, v = constant volume)} \end{equation} \begin{equation} \Lambda = \frac{C_p}{C_v} \qquad \textnormal{(Ratio of capacities)} \end{equation}
\begin{equation} W = n \, C_v (T_1 - T_2) = \frac{C_v}{R} (p_1 V_1 - p_2 V_2) = \frac{1}{\gamma - 1} (p_1 V_1 - p_2 V_2) \qquad \textnormal{(Work done by gas)} \end{equation}
Next module Gases