Thermodynamics Formulas: Control Volume, Heat Transfer, Polytropic Process, Substance Prop, Study notes of Thermodynamics

Download Thermodynamics Formulas: Control Volume, Heat Transfer, Polytropic Process, Substance Prop and more Study notes Thermodynamics in PDF only on Docsity! ME 3322 Thermodynamics – Formula Sheet Page 1 Control Volume Balance Equations (uniform flow) Mass, m outin mmdt dm −= Energy, E ( ) ( )2 21 12 2in out in outin out dE Q W m h V gz m h V gz dt = − + + + − + + Entropy, S , 0in in in out out b QdS m s m s dt T σ σ= + − + ≥ Heat Transfer Rate Equations Conduction dx dTAQx κ−= , positive in the positive x-direction Convection ( )fbc TThAQ −= , positive from the surface to the surroundings Radiation 4be ATQ εσ= , positive from the surface to the surroundings Polytropic Process Equations constantorconstant == nn pvpV nn v v p p V V p p ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ =⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = 2 1 1 2 2 1 1 2 or Efficiency and Coefficient of Performance (COP) of a Cyclic Process Definition Power Refrigeration Heat Pump inputrequired outputdesired,, =γβη H net Q W =η net C W Q =β net H W Q =γ Carnot (maximum) value H CH T TT − =η CH C TT T − =β CH H TT T − =γ Isentropic Efficiencies turbine: s t t w w =η compressor: c s c w w =η nozzle: 2 2 s n n V V =η Constants Units Standard atmosphere: 1 atm = 101.3 kPa Standard gravity: g = 9.807 m/s2 Temperature relation: T(K) = T(ºC) + 273.15 K Universal gas constant: K).kJ/(kmol 314.8=R Gas constant, air: R = 0.287 kJ/(kg.K) Molecular weight, air: M = 28.97 kg/kmol 1 bar = 100 kPa W = J/s J = N.m N = kg.m/s2 Pa = N/m2