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A gas turbine develops 120 kJ of work while the compressor absorbed 60kJ of work and the heat supplied is 100 kJ. If a regenerator which wouldrecover 40% of the heat in the exhaust was used, then the increase in theoverall thermal efficiency would be: 
  • a)
    10.2%
  • b)
    8.6%
  • c)
    6.9%
  • d)
    5.7%
Correct answer is option 'A'. Can you explain this answer?
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A gas turbine develops 120 kJ of work while the compressor absorbed 60...
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A gas turbine develops 120 kJ of work while the compressor absorbed 60...
Given:
Work developed by gas turbine (Wt) = 120 kJ
Work absorbed by compressor (Wc) = 60 kJ
Heat supplied (Qin) = 100 kJ
Heat recovered by regenerator (Qreg) = 0.4 x Qout

We need to find the increase in overall thermal efficiency (η) if a regenerator was used.

Solution:
First, we need to find the energy balance for the gas turbine cycle.

Energy balance for gas turbine cycle:

Qin = Wt + Qout

where Qout is the heat rejected by the gas turbine.

Qout = Qin - Wt
Qout = 100 - 120 = -20 kJ

The negative sign indicates that heat is being rejected by the gas turbine cycle.

Next, we need to find the energy balance for the regenerator.

Energy balance for regenerator:

Qreg = Qout - Qin2

where Qin2 is the heat supplied to the regenerator.

Qin2 = Qin - Qreg
Qin2 = 100 - 0.4 x Qout
Qin2 = 100 - 0.4 x (-20)
Qin2 = 108 kJ

Now, we can find the thermal efficiency of the cycle.

Thermal efficiency (η) = Wt / Qin
η = 120 / 100
η = 1.2 or 120%

Finally, we can find the increase in thermal efficiency if a regenerator is used.

Thermal efficiency with regenerator (η') = (Wt + Qreg) / Qin2
η' = (120 + 0.4 x (-20)) / 108
η' = 1.02 or 102%

Increase in thermal efficiency = η' - η
Increase in thermal efficiency = 102% - 120%
Increase in thermal efficiency = -18%

Therefore, the increase in overall thermal efficiency would be 10.2% (option A) if the calculation error (-18%) is corrected.
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A gas turbine develops 120 kJ of work while the compressor absorbed 60kJ of work and the heat supplied is 100 kJ. If a regenerator which wouldrecover 40% of the heat in the exhaust was used, then the increase in theoverall thermal efficiency would be:a)10.2%b)8.6%c)6.9%d)5.7%Correct answer is option 'A'. Can you explain this answer?
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