An Inventor claims to have developed an isothermal, steady-flow turbine capable

Question

An Inventor claims to have developed an isothermal, steady-flow turbine capable of producing 100 kW when operating with a steam flow rate of 10,600 lb/hr. The inlet conditions are 500 psia and 1000 F and the exit pressure is 14.7 psia. Heating takes place as the steam flows through the turbine to maintain (a) the heat required and (b) the numerical value for each term in an entropy balance. Then evaluate the inventor's claim


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Explanation / Answer

1kW = 3412 Btu/hr
100kW = 341200 Btu/hr
Power=m_dot*wturbine => 341200 = 10600(wturbine)

wturbine= 32.189 Btu/lb

Steam at turbine inlet: P1=500 psia T1=1000F h1=1520.30 Btu/lb   s1=1.7375 Btu/lbF
Steam at turbine exit: P2=14.7 psia T2=1000F h2= 1534.90 Btu/lb s2=2.1334 Btu/lbF

First law

Heat required = m_dot*(h2-h1+wturbine) = 10600(1534.90-1520.30+32.189)

= 495963 Btu/hr = 145.36 kW

Second law

Entropy generation = m_dot(s2-s1)-Q/T = 10600(2.1334-1.7375)-495963/(1000+459.67) = 3856.76 > 0 OK

This machine can operate without violating second law of thermodynamics

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