# FE thermo - THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT...

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56 THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT SYSTEMS Nomenclature 1. Intensive properties are independent of mass. 2. Extensive properties are proportional to mass. 3. Specific properties are lower case (extensive/mass). State Functions (properties) Absolute Pressure, p (lbf / in 2 or Pa) Absolute Temperature, T ( ° R or K) Specific Volume, v (ft 3 / lbm or m 3 / kg) Internal Energy, u (usually in Btu / lbm or kJ / kg) Enthalpy, h = u + Pv (same units as u ) Entropy, s [Btu / (lbm- ° R) or kJ / (kg K)] Gibbs Free Energy, g = h Ts (same units as u ) Helmholz Free Energy, a = u Ts (same units as u ) Heat Capacity at Constant Pressure, P p T h c = Heat Capacity at Constant Volume, v v T u c = Quality x (applies to liquid-vapor systems at saturation) is defined 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. Specific volume of a two-phase system can be written: v = xv g + (1 – x ) v f or v = xv fg + v f , where v f = specific volume of saturated liquid, v g = specific volume of saturated vapor, and v fg = specific volume change upon vaporization. = v g v f Similar expressions exist for u , h , and s : u = xu g + (1 – x ) u f h = xh g + (1 – x ) h f s = xs g + (1 – x ) s f For a simple substance, specification of any two intensive, independent properties is sufficient to fix 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 = specific volume, m = mass of gas, R = gas constant, and T = absolute temperature. R is specific to each gas but can be found from () wt. mol. R R = , where = 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 : 0 0 = = T T ν u v h For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true: u = c v T ; h = c P T s = c P ln ( T 2 /T 1 ) – R ln ( P 2 /P 1 ); and 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 h is known as the mean heat capacity ( ) and is given by 1 2 2 1 T T dT c c T T p p = Also, for constant entropy processes: P 1 v 1 k = P 2 v 2 k ; T 1 P 1 (1– k )/ k = T 2 P 2 (1– k )/ k T 1 v 1 ( k –1) = T 2 v 2 ( k –1) , where k = c p / c v 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. Heat Q is energy transferred due to temperature difference and is considered positive if it is inward or added to the system. Closed Thermodynamic System No mass crosses system boundary Q W = U + KE + PE where KE = change in kinetic energy, and PE = change in potential energy.

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FE thermo - THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT...

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