Basic Thermodynamic Formulas Exam Equation Sheet, Cheat Sheet of Applied Thermodynamics

Download Basic Thermodynamic Formulas Exam Equation Sheet and more Cheat Sheet Applied Thermodynamics in PDF only on Docsity! Basic Thermodynamic Formulas (Exam Equation Sheet) Control Mass (no mass flow across system boundaries) Conservation of mass: 𝑚 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Conservation of energy (1st Law): � 𝑄 −𝑊 = ∆𝐸 = ∆𝑈 + ∆𝐾𝐸 + ∆𝑃𝐸 = 𝑚�∆𝑢 + 𝑣2 2−𝑣12 2 + 𝑔(𝑧2 − 𝑧1)� Entropy Balance (2nd Law): ∆𝑆 = ∫ �𝛿𝛿𝑇 �𝑏 + 𝜎 Control Volume (mass flow across system boundaries) Conservation of mass: 𝑑𝑚𝐶𝐶 𝑑𝑑 = ∑ ?̇?𝑖 −∑𝑚𝑒̇ ; where ?̇? = 𝐴𝑉� 𝜈 is the mass flow rate Conservation of energy (1st Law): 𝑑𝐸𝐶𝐶 𝑑𝑑 = ?̇? − ?̇? + ∑ ?̇?𝑖 �ℎ𝑖 + 𝑉𝑖 2 2 + 𝑔𝑧𝑖� −∑ ?̇?𝑒 �ℎ𝑒 + 𝑉𝑒2 2 + 𝑔𝑧𝑒� Entropy Balance (2nd Law): 𝑑𝑆𝐶𝐶 𝑑𝑑 = ∑ ?̇?𝑘 𝑇𝑘 + ∑?̇?𝑖𝑐𝑖 −∑ ?̇?𝑒𝑐𝑒 + ?̇?𝐶𝑉 Heat Transfer and Work Relationships Conduction: ?̇? = −𝑘𝑘 𝑑𝑇 𝑑𝑑 Convection: ?̇? = ℎ𝑘(𝑇𝑠 − 𝑇∞) Radiation: ?̇? = 𝜀𝜎𝑘(𝑇𝑠4 − 𝑇𝑠𝑠𝑠4 ) Heat transfer for an internally reversible process: 𝑄𝑖𝑖𝑑.𝑠𝑒𝑣 = ∫𝑇 𝑑𝑆 Boundary work: 𝑊𝑏 = ∫𝑃𝑑𝑃 Polytropic process: � 𝑃𝑃𝑖 = 𝐶𝑐𝑐𝑐𝑐 𝑐 = 1,𝑊𝑏 = 𝑃1𝑃1𝑙𝑐 𝑉2 𝑉1 𝑐 ≠ 1,𝑊𝑏 = 𝑃2𝑉2−𝑃1𝑉1 1−𝑖 � Polytropic process for Ideal Gas: � 𝑇2 𝑇1 = �𝑃2 𝑃1 � (𝑖−1)/𝑖 𝑇2 𝑇1 = �𝑉1 𝑉2 � 𝑖−1 � Reversible steady flow work: 𝑤𝑠𝑒𝑣 = −∫𝑣𝑑𝑃 + 𝑣12−𝑣22 2 + 𝑔(𝑧1 − 𝑧2) Ideal gas, no change in kinetic and potential energy Isentropic: 𝑤𝑠𝑒𝑣 = 𝑘𝑘(𝑇1−𝑇2) 𝑘−1 = 𝑘𝑘𝑇1 𝑘−1 �1 − �𝑃2 𝑃1 � �𝑘−1𝑘 �� Isothermal: 𝑤𝑠𝑒𝑣 = 𝑅𝑇𝑙𝑐 � 𝑃1 𝑃2 � Polytropic: 𝑤𝑠𝑒𝑣 = 𝑖𝑘(𝑇1−𝑇2) 𝑖−1 = 𝑖𝑘𝑇1 𝑖−1 �1 − �𝑃2 𝑃1 � �𝑛−1𝑛 ��