Thermodynamics Equation Sheet PDF

Ideal Gas Equation Pv = RT or PV = mRT where R = Ru/MW Specific Gas Constant Rair = 0.287 kJ/kg∙K = 0.287 kPa∙m3/kg∙K (use table A-1 for other gases) Mass Balance: Open dmsys = ∑ m − ∑ m...

Ideal Gas Equation Pv = RT or PV = mRT where R = Ru/MW Specific Gas Constant Rair = 0.287 kJ/kg∙K = 0.287 kPa∙m3/kg∙K (use table A-1 for other gases) Mass Balance: Open dmsys = ∑ m − ∑ m i o m = ρVA for 1-D flows dt inlets outlets Energy Balance: dE sys  dE sys d Open = Ein − E out = [U + PE + KE ] dt where dt dt dE sys =(Q in + Win ) − (Q out + Wout ) + ∑ m i (hi + Vi 2 / 2 + gzi ) − ∑ m (h o o + Vo2 / 2 + gzo Open (Expanded) dt inlets outlets ∆Esys = Ein − Eout ∆Esys = ∆U + ∆KE + ∆PE Closed where Closed (Expanded) ∆Esys = (Qin + Win ) − (Qout + Wout ) Entropy Balance: dS sys Open =Sin − Sout + Sgen dt where Ṡin an Ṡout can be mass, heat transfer, or both ∆S = Sin − Sout + S gen Closed where Sin and Sout are only heat transfer (i.e. not mass) Entropy Changes of= T   P2   T2   v2  ∆s C p ln  2  − R ln  =  ∆s Cv ln   + R ln   Ideal Gases:  T1   P1  or  T1   v1  NOTE: This assumes constant specific heats.  k −1    Isentropic process, T2  P2   k  PG model T1v1k −1 = T2 v2k −1 1 1 = P2 v2 Pv k k =  T1  P1  Different Types of W = ∫ F ⋅ ds w = ∫ Pdv (Specific) W = m ∫ Pdv (Total) Work: General: Boundary: Welec =V *I W = 2π nT  Shaft: shaft Electrical: w = ∫ vdP (Specific) Ẇ = ṁ ∫ vdP (Total) Reversible Steady Flow Work: wnet ,out qout qin 1 η HE = COP = == 1− win 1 − qin qout R qin qin Efficiency and COP qout 1 COP= = win qout qin − 1 HP Properties h = u + Pv or H = U + PV du = cvdT dh = cpdT cp = cv + R For any property, Y = my (upper case is total, lower case is specific) x= m vapor , vx = vf + x(vg-vf) , ux = uf + x(ug - uf), hx = hf + x(hg - hf) m liquid + m vapor