Equation sheet for Thermodynamics | ME 2334, Study notes of Thermodynamics

Download Equation sheet for Thermodynamics | ME 2334 and more Study notes Thermodynamics in PDF only on Docsity! BASIC EQUATIONS FOR ME 200 (1) Work and Energy Relations  pdVWb tVIWe  )xx(2 k W 21 2 2 s spring  2rotW n  2 2 2 1 2 1 2 1 ( ) / 2 ( )cvw dp V V g z z        2 22 1ΔKE = 0.5m V -V  2 1ΔPE = mg z -z spring sF = k x (2) First Law Relations and Mass Conservation Q W U KE PE        2 2 cvcv cv e ie i e i dE Q -W - m h+V /2+gz + m h+V /2+gz = dt   m=ρVA m V  cvi e i e dm m - m = dt   (3) Second Law Relations         b 2 1 T Q S revint 2 1 T q s         dS dt Q T j jj              m s m s Q T dS dt e e e i i i j j cv j cv b δQ -σ 0 T         PROPERTY RELATIONS FOR ME 200 (4) Pressure, Temperature and Energy Relations p p pabs atm gage  p p gLatm   m V  pV nRT pV mRT R R M P ZRT  cR p/pp  cR T/TT  /R c cp RT   p vk C /C )mm/(mx gfg  fgfgf xyyxyy)x1(y  fgfg yyy  h u Pv  dTcu v dTch p p vC -C R dTcu  h u p    f f sath T p h T T p - p T          fu(T,p) u (T) fT p T       fs(T,p) s (T) (5) Entropy Relations (and Isentropic Processes) Tds du pd   Tds dh dp  2 2 1 1 ln lnv T s c R T      2 2 1 1 ln lnp T p s c R T p    )p/pln(Rsss 12 o 1 o 2  )T/Tln(cs 12     ( 1)/ 1 2 1 2 1 1 2/ / / k k k T T p p         1r2rs12 p/pp/p   2 1 2 1/ /r rs     EFFICIENCY AND CYCLE RELATIONS FOR ME 200 (6) Device Efficiencies and Cycle Analyses turbine act isenw w  compressor pump isen actw w    net,out th in W η = Q inR net,in Q COP = W outHP net,in Q COP = W pump turbine w BWR w  C th,rev H T η =1- T C R,rev H C T COP = T -T HHP,rev H C T COP = T -T revH C H C Q Q T T        UNITS CONVERSION TABLE FOR ME 200 Mass and Density 1 2.20kg lb m  1 10 3 3 3 g cm kg m 3 3 1 62.4g cm lb ft m  1 0.454lb kg m  3 3 1 16.018lb ft kg m m  Length 1 0.394cm in 1 3.28m ft 1 2 54in cm . 1 0.305ft m Velocity 1 0.621km h mile h 1 1.61mile h km h Volume 3 3 1 0.061cm in 3 3 1 35.3m ft 1 10 3 3 L m  3 1 0.035L ft 3 3 1 16.4in cm 3 3 1 0.0283ft m 3 1 0.134gal ft 3 3 1 3.79 10gal m    Force 1 1 2 N kg m s  1 0.224N lb f  2 1 32.2lb lb ft s f m   1 4.45lb N f  Pressure 2 4 2 1 1 1.45 10Pa N m lb in f     1 10 5 2 bar N m 1 1.01atm bar 2 1 6894.8lb in Pa f  2 2 1 144lb in lb ft f f  2 1 14.7atm lb in f  Energy and Specific Energy 1 1 0.738J N m ft lb f     1 737.56kJ ft lb f   1 0.948kJ Btu 1 0.43kJ kg Btu lb m  1 1.36ft lb J f   1 778.17Btu ft lb f   1 1.055Btu kJ 1 2.326Btu lb kJ kg m  1 4.19kcal kJ Energy Transfer Rate 1 1 3 413W J s Btu h  . 1 1 341kW hp . 1 0 293Btu h W . 1 2545hp Btu h 1 550hp ft lb s f   1 0.746hp kW 1 ton =12,000Btu/h=3.517kW Specific Heat 1 0.239kJ kg K Btu lb R m    1 1kcal kg K Btu lb R m    1 4.19Btu lb R kJ kg K m   Universal Gas Constant 8.314 / 1545 / 1.986 / o f o kJ kmol K R ft lb lbmol R Btu lbmol R         Standard Acceleration of Gravity 2 2 9.81 / 32.174 / m s g ft s     Standard Atmospheric Pressure 2 1.01 1 14.7 /     f bar atm lb in Temperature Relations )K(T8.1)R(T o  ( ) ( ) 273oT C T K  ( ) ( ) 460o oT F T R 