Fe-Thermo - THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT...

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73 THERMODYNAMICS ±THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT SYSTEMS Nomenclature 1. Intensive properties are independent of mass. 2. Extensive properties are proportional to mass. 3. Speci f c properties are lowercase (extensive/mass). State Functions (properties) Absolute Pressure, P (lbf / in 2 or Pa) Absolute Temperature, T ( ° R or K) Volume, V (ft 3 or m 3 ) Speci f c Volume, vVm = (ft 3 / lbm or m 3 / kg) Internal Energy, U (Btu or kJ) Speci f c Internal Energy, uUm = (usually in Btu / lbm or kJ / kg) ±Enthalpy,± H (Btu or KJ) Speci f c Enthalpy, h = u + Pv = H/m (usually in Btu / lbm or kJ / kg) Entropy, S (Btu / ° R or kJ / K) Speci f c Entropy, s = S/m [Btu /( lbm- ° R) or kJ / (kg•K)] Gibbs Free Energy, g = h Ts (usually in Btu / lbm or kJ / kg) Helmholz Free Energy, a = u (usually in Btu / lbm or kJ / kg) Heat Capacity at Constant Pressure, c T h p P 2 2 = bl Heat Capacity at Constant Volume, c T u v v 2 2 = Quality x (applies to liquid-vapor systems at saturation) is de f ned as the mass fraction of the vapor phase: x = m g / ( m g + m f ) , where m g = mass of vapor, and m f = mass of liquid. Speci f c volume of a two-phase system can be written: v = xv g + (1 – x ) v f or v = v f + xv fg , where v f = speci f c volume of saturated liquid, v g = speci f c volume of saturated vapor, and v fg = speci f c volume change upon vaporization. = v g v f Similar expressions exist for u , h , and s : u = xu g + (1 – x ) u f or u = u f + xu fg h = xh g + (1 – x ) h f or h = h f + xh fg s = xs g + (1 – x ) s f or s = s f + xs fg For a simple substance, speci f cation of any two intensive, independent properties is suf f cient to f x all the rest. For an ideal gas, Pv = RT or PV = mRT , and P 1 v 1 /T 1 = P 2 v 2 /T 2 , where P = pressure, v = speci f c volume, m = mass of gas, R = gas constant, and T = absolute temperature. V = volume R is speci f c to each gas but can be found from . , R mol wt R where = ^h R = the universal gas constant = 1,545 ft-lbf/(lbmol- ° R) = 8,314 J / (kmol K). For ideal gases , c p c v = R Also, for ideal gases : P h v u 00 TT 2 2 2 2 == bb ll For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true: Δ u = c v Δ T ; Δ h = c p Δ T Δ s = c p ln ( T 2 /T 1 ) – R ln ( P 2 /P 1 ); and Δ s = c v ln ( T 2 /T 1 ) + R ln ( v 2 /v 1 ). For heat capacities that are temperature dependent, the value to be used in the above equations for Δ h is known as the mean heat capacity c p `j and is given by c cdT p p T T 21 1 2 = - # Also, for constant entropy processes: ; , P P v v T T P P T T v v kcc where k k k k pv 1 2 2 1 1 2 1 2 1 1 2 2 1 1 - - d d d n n n For real gases, several equations of state are available; one such equation is the van der Waals equation with constants based on the critical point: , P v a vb R T a P RT b P RT 64 27 8 where 2 c c c c 2 2 +- = c ^ c f m h m p where P c and T c are the pressure and temperature at the critical point, respectively, and v is the molar speci f c volume.
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74 THERMODYNAMICS FIRST LAW OF THERMODYNAMICS The First Law of Thermodynamics is a statement of conservation of energy in a thermodynamic system. The net energy crossing the system boundary is equal to the change in energy inside the system.
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Fe-Thermo - THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT...

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