Chapter 5 problems often combine mass/energy balances from Chapter 4 (First Law) with entropy balances.
Chapter 5 of "Thermodynamics" by Hipolito Sta. Maria delves into the second law of thermodynamics, which is a fundamental principle in understanding the behavior of energy and its interactions with matter. The second law of thermodynamics states that the total entropy of an isolated system always increases over time, except in reversible processes. This chapter explores the concept of entropy, the Clausius inequality, and the Kelvin-Planck statement.
| Symbol | Definition | Equation | |--------|------------|----------| | ( \Delta s ) | Specific entropy change | ( \Delta s = \int_1^2 \frac\delta q_\textrevT ) | | ( s_\textgen ) | Entropy generation rate | ( \dot S_\textgen = \dot S_\textout - \dot S_\textin + \sum \frac\dot Q_kT_k ) | | ( \eta_\textCarnot ) | Carnot thermal efficiency | ( \eta = 1 - \fracT_cT_h ) | | ( \textCOP R ) | Coefficient of performance (refrigerator) | ( \textCOP R = \fracQ_LW \textnet = \frac1\fracT_hT_L - 1 ) | | ( \psi ) | Specific exergy | ( \psi = (u-u_0) + p_0(v-v_0) - T_0(s-s_0) ) | | ( \dot E \textdestroy ) | Exergy destruction rate | ( \dot E_\textdestroy = T_0 \dot S_\textgen ) | | ( \Delta h_\textthrottling ) | Enthalpy change across a valve | ( h_2 = h_1 ) (isenthalpic) |
For , (\delta Q = 0) → (S_2 - S_1 = S_gen \ge 0). If reversible adiabatic → isentropic ((S_1 = S_2)).
From entropy balance (control volume, steady, adiabatic, 1-in 1-out): [ s_2a - s_1 = s_gen \quad (\textsince \dotQ=0, \dotm=1) ] Thus (s_gen = s_2a - s_1) in kJ/kg·K. Must be > 0.