[[Thermodynamics]] For specific unit operations, see [[Process Energy Balances]] ## Energy Balance Equations: | | Const P | Const V | Const T | Rev. Adiabatic | | ----- | ------------------------------------- | -------------------------------------------- | ------------------------------ | ----------------------- | | W | $-P(V_2 - V_1)$ | $0$ | $W = nRTln(\frac{V_2}{V_1})$ | $ΔU$ | | Q | $ΔH$ | $ΔU$ | $-W (Reversible: TΔS)$ | $0$ | | ΔU | $Q+W = \int_{T1}^{T2}C_VdT$ | $\int_{T1}^{T2}C_VdT$ | $0$ | $\int_{T1}^{T2}C_VdT$ | | ΔH | $\int_{T1}^{T2}C_PdT$ | $\int_{T1}^{T2}C_PdT$ | $0$ | $\int_{T1}^{T2}C_PdT$ | | ΔS | $\int_{T1}^{T2}C_PdT$ | $\int_{T1}^{T2}C_PdT-Rln(\frac{P_2}{P_1})$ | $-Rln(\frac{P_2}{P_1})$ | $0$ | | State | $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ | $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ | $P_1V_1 = P_2V_2$ | $(\frac{P_2}{P_1}) = (\frac{T_2}{T_1})^{R/C_P} = (\frac{V_1}{V_2})^{R/C_P}$ | ### Definitions: #### [[Work (W) is energy transfer]] Sign convention: (+) from system to surroundings, (-) from surroundings to system #### [[Heat (Q) is energy transferred between systems at different temperatures]] Sign convention: (+) from surroundings to system, (-) from system to surroundings #### [[Internal Energy (U) of a system is its total energy content]] #### [[Enthalpy (H) is the heat energy of a system]] #### [[Heat Capacity (Cp, Cv) is the amount of heat needed to raise the temperature of a substance]]