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Question

A calorically perfect gas (specific heat at constant pressure 1000 J/kgK) enters and leaves a gas turbine with the same velocity. The temperature of the gas at turbine entry and exit are 1100 K and 400 K, respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is

A
6.14
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B
7.00
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C
7.50
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D
8.00
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Solution

The correct option is B 7.00
(b)
cp=1kJ/kgK

Vi=Ve (Inlet and exit velocity same)
Wcv=4.6MW=4.6×103kW
Applying SFEE,
m(hi+12v2i+gzi+Q=m(he+12v2e+gze+Wcv
m[cp(TiTe)]+Q=Wc.v. (Letzi=ze)
m[1×(1100400)]+(300)=4.6×103
m=7kg/s

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