Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 9, Problem 177RQ

a)

To determine

The thermal efficiency and the required mass flow rate of helium when the isentropic efficiency is 100%.

a)

Expert Solution
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Explanation of Solution

Given:

Pressure ratio (rp) is 8.

Net power output (W˙net) is 60MW.

Effectiveness (ε) is 0.75.

Compressor inlet temperature (T1) is 300K.

Turbine inlet temperature (T3) is 1800K.

Calculation:

Draw the Ts diagram of the cycle as in Figure (1).

Fundamentals Of Thermal-fluid Sciences In Si Units, Chapter 9, Problem 177RQ

Refer Table A-2, “Ideal-gas specific heats of various common gases”, obtain the properties of the helium.

  cp=5.1926kJ/kgKk=1.667

Calculate the temperature at state 2s(T2s).

  T2s=T1(P1P2)k1k=T1(rP)k1k=(300K)(8)1.66711.667=689.4K

Calculate the temperature at state 4s(T4s).

  T4s=T3(P4P32)k1k=T3(1rP)k1k=(1800K)(18)1.66711.667=783.3K

Calculate the temperature at state 5(T5).

  T5=T2+ε(T4T2)=689.4K+(0.75)(783.3K689.4K)=759.8K

Calculate the mass flow rate of the helium (m˙).

  m˙=W˙netwnet=W˙netcp[(T3T4)(T2T1)]=60,000kJ/s(5.1926kJ/kgK)[(1800K783.3K)(689.4K300K)]=18.42kg/s

Thus, the mass flow rate of the helium is 18.42kg/s.

Calculate the thermal efficiency of the cycle (ηth).

  ηth=wnetqin=cp[(T3T4)(T2T1)]cp[(T3T5)]

  =(1800K783.3K)(689.4K300K)1800K759.8K=0.603=60.3%

Thus, the thermal efficiency of the cycle is 60.3%.

b)

To determine

The thermal efficiency and the required mass flow rate of helium when the isentropic efficiency is 80%.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the temperature at state 2s(T2s).

  T2s=T1(P1P2)k1k=T1(rP)k1k=(300K)(8)1.66711.667=689.4K

Calculate the temperature at state 2(T2).

  T2=T1+(T2sT1)ηC=300K+(689.4K300K)0.80=786.8K

Calculate the temperature at state 4s(T4s).

  T4s=T3(P4P32)k1k=T3(1rP)k1k=(1800K)(18)1.66711.667=783.3K

Calculate the temperature at state 4(T4).

  T4=T3ηT(T4sT3)=1800K(0.80)(1800K783.3K)=986.6K

Calculate the temperature at state 5(T5).

  T5=T2+ε(T4T2)=786.8K+(0.75)(986.6K786.8K)=936.7K

Calculate the mass flow rate of the helium (m˙).

  m˙=W˙netwnet=W˙netcp[(T3T4)(T2T1)]=60,000kJ/s(5.1926kJ/kgK)[(1800K986.6K)(786.8K300K)]=35.4kg/s

Thus, the mass flow rate of the helium is 35.4kg/s.

Calculate the thermal efficiency of the cycle (ηth).

  ηth=wnetqin=cp[(T3T4)(T2T1)]cp[(T3T5)]

  =(1800K986.6K)(786.8K300K)1800K936.7K=0.378=37.8%

Thus, the thermal efficiency of the cycle is 37.8%.

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Chapter 9 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

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