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2.5 2 1.5 1 300 400 500 600 700 800 900 temperature T(K) 1000 1100 1200 1300 Specific heat at constant pressure as function of temperature H2O Air Figure 14: Specific heat capacity for air (dashed red) and water vapor (dotted blue), Cengel (1998). Note in figure 14, the larger heat capacity of water vapor, which makes the mass percentage of water vapor in air an important variable. When we use a constant specific heat, we use the average of the value at the inlet and the outlet of the compressor. Integration gives: T −w=cp,avg(T2 −T1)=cp,avgT1 2 −1 1 Another way to calculate cp is taken from Philip (1999): cp =( κ )R κ −1 (5.1.5) (5.1.6) T where κ (sometimes denoted k) is the ratio of the specific heat at constant pressure and constant volume. R is the gas constant for the specified gas, in this case air. Note that κ also varies with temperature, but not as much as cp, since the variations of cp and cv, due to temperature, almost cancel each other. The value of κ is taken as the average of the inlet and the outlet of the compressor, but the subscript is from now on dropped. Then our equation for the work can be rewritten as: κT −w=( )RT1 2 −1 (5.1.7) κ −1 T 1 Of the parameters above, only T2 varies, since T1 is the inlet temperature and R and κ are approximately constant. The work is at minimum, when T2 is minimal. This is achieved at isentropic compression. Isentropic means that the process is adiabatic (no heat flows in or out of the system) and reversible (the process can be reversed without losing energy, e.g. no friction). 23 specific heat at constant pressure Cp(kJ/kg K)PDF Image | Modelling of Microturbine Systems
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