Solution_to_HW_7

# Solution_to_HW_7 - ENGR 301 F2009 HW 7 Due on Monday Note...

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ENGR 301 F2009 HW 7 Due on Monday, November 23, 2009. Note: Isentropic efficiency of an adiabatic turbine = (h in – h out,s ) / (h in – h out,a ) = w s / w a Where w s and h out,s are the work output and exit stream enthalpy under isentropic (i.e. reversible adiabatic) conditions, w a and h out,a are the actual work output and exit stream enthalpy of the irreversible adiabatic turbine. Isentropic means s in = s out . Isentropic efficiency of an adiabatic compressor = (h out,a – h in ) / (h out,s – h in ) = w a / w s Where w s and h out,s are the work input and exit stream enthalpy under isentropic (i.e. reversible adiabatic) conditions, w a and h out,a are the actual work input and exit stream enthalpy of the irreversible adiabatic compressor. The isentropic compression work input, w s , is equal to (h out,s – h in ) = dP out in υ Since liquids are incompressible, ) P - (P w in out s υ = where υ is specific volume of liquid at inlet temperature. The actual compression work input, w a , is equal to (h out,a – h in ).

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T = 95 0 F = 555 R Δ S FLUID = - 0.7 Btu/R (a) Assuming friction free and quasi-equilibrium process, Heat transferred to the fluid = T . Δ S FLUID = (555 R) (-0.7 Btu/R) = -388.5 Btu Negative sign indicated that heat is transferred out of the fluid. Heat transferred to sink = 388.5 Btu (b) Temperature of sink = 95 0 F = 555 R Æ Change in entropy of sink = Heat in / T sink = (388.5 Btu)/(555 R) = + 0.7 Btu/R (c) Total change in entropy = Change in entropy of fluid + Change in entropy of sink = 0 Btu/R The total change is zero because heat transfer is taking place in absence of any temperature differential. Hence the process is reversible.
Fluid: R-134a System: Turbine Æ open system, assume reversible and at steady state Process: Isentropic Æ S 1 = S 2 Inlet – state 1: P 1 = 250 psia, T 1 = 175 0 F From table A-12E, T sat at 170 0 F = 113.69 psia and T sat at 170 0 F = 117.69 psia Î By interpolation, T sat at 175 0 F = 115.69 psia < 250 psia Î The fluid is superheated. Table A-13E will be used to calculate specific entropy at inlet. It requires double interpolation.

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Solution_to_HW_7 - ENGR 301 F2009 HW 7 Due on Monday Note...

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