Question

Problem 9.49: Air enters the turbine of a gas turbine at 1200 kPa, 1200 K, and expands to 100 kPa in two stages. Between the stages, the air is reheated at a constant pressure of 350 kPa to 1200 K. The expansion through each turbine stage is isentropic. Determine, in kJ per kg of air flowing, (a.) the work developed by each stage. (b.) the heat transfer for the reheat process. (c.) the increase in net work as compared to a single stage of expansion with no reheat.

Answer 1

Answer

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Step-by-step explanation:

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Answer 2

The work developed is:365.67kj/kg; 370.94 kj/kg and the heat transfer is: 365.67 kj/kg and the increase in net work is: 97.42 kj/kg.

kJ per kg of air flowing

wI=h3-h2

T3=1200 K

h3=1277.79 kj/kg

Pr3=238

Pra/Pr3=P4/P3=350/1200

Pra=350/1200×238

Pra=69.42

ha=912.12 kj/kg

wI=1277.79-912.12

wI=365.67kj/kg

wII=h5-h6

h5=h3=1277.79 kj/kg ;Pr5=238

Pr6/Pr5=P6/P5=100/350

Pr6=100/350×238

Pr6=68

h6=906.85 kj/kg

wII=1277.79-906.85

wII=370.94 kj/kg

b. Reheat=h5-h4

Reheat=1277.79-312.12

Reheat=365.67 kj/kg

c. Single stage expansion

Pr4/Pr3=P4/P3=100/1200

Pr4=100/1200×238

Pr4=19.83

h4=638.6 kj/kg

w=h3-h4

w=1277.79-638.6

w=639.19 kj/kg

Double stage expansion

w=wI+wII

w=365.67 kj/kg+370.94 kj/kg

w=736.61 kj/kg

Difference in work=736.61 kj/kg-639.19 kj/kg

Difference in work=97.42 kj/kg

Therefore the work developed is:365.67kj/kg; 370.94 kj/kg and the heat transfer is: 365.67 kj/kg and the increase in net work is: 97.42 kj/kg.

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