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COMPENDIUM OF EQUATIONS Unified Engineering Thermodynamics I. Equation of State: pv = RT or p = RT for a thermally perfect gas II. Expressions for Work: A. Work for a simple compressible substance W = p ext dV V 1 V 2 B. Work for a simple compressible substance undergoing a quasi-static process W = pdV V 1 V 2
Entropy Balance (2nd Law): ∆𝑆= ∫ 𝛿𝛿 𝑇 𝑏 + 𝜎. Control Volume (mass flow across system boundaries) Conservation of mass: 𝑑𝑚𝐶𝐶 𝑑𝑑 = ∑𝑚̇𝑖−∑𝑚𝑒̇; where 𝑚̇= 𝐴𝑉 𝜈 is the mass flow rate Conservation of energy (1st Law): 𝑑𝐸𝐶𝐶 𝑑𝑑 = 𝑄̇−𝑊̇+ ∑𝑚̇
Variation of pressure with depth: Apply between two points in the same fluid. Where “below” refers to point at lower elevation and “above” at higher elevation. 1 2 x and x are the initial and final displacements of the spring. During actual exp/comp process of gases, P and V are related by PVn=C.
Specific Energy, Q Q= Q +𝑥( Q − ) Specific Entropy, O O= O +𝑥( O − ) Specific Volume, R R= R Volume Flow Rate, ̇ +𝑥( R − R ) • is the density • is the speed • 𝐴 is the cross-sectional area of the duct • R is the specific volume -= A picture containing icon
Free online university thermodynamics cheat sheet with key equations needed to solve thermodynamic processes.
Reversible Adiabatic (Isentropic Process): Entropy decrease in process 3-4 = the entropy increase in process 1-2. Reversible Heat-Transfer Process Entropy Generation
The specific entropy of an ideal gas is a function of both temperature and pressure. Here we will introduce a simplified method for calculating the change of the specific entropy of an ideal gas in a process by assuming constant specific heats.
