Consider a simple ideal Brayton cycle with air as the working fluid. The pressure ratio of the cycle is 6, and the minimum and maximum temperatures are 300 and 1300 K, respectively. Now the pressure ratio is doubled without changing the minimum and maximum temperatures in the cycle. Determine the change in (a) the net work output per unit mass and (b) the thermal efficiency of the cycle as a result of this modification. Assume variable specific heats for air.
a)
The change in net work output per unit mass.
Answer to Problem 164RP
The change in net work output per unit mass is
Explanation of Solution
Draw the
Write the expression for the pressure ratio in terms of relative pressure to calculate the relative pressure at state 2
Here, compressor inlet pressure is
Write the expression for the pressure ratio in terms of relative pressure to calculate the relative pressure at state 4
Here, compressor inlet pressure is
Write the expression for the heat added
Here, specific enthalpy of air from the exit of compressor is
Write the expression for the heat rejected
Here, specific enthalpy of air at the exit of the turbine is
Write the expression for net work done
Write the expression for net work done
Write the expression for the thermal efficiency
Write the expression for the thermal efficiency
Write the expression for change in the net work
Here, net work done for the initial cycle is
Conclusion:
For relative pressure
From the Table A-17, “Ideal-gas properties of air” obtain the following properties at temperature
From the Table A-17, “Ideal-gas properties of air” obtain the following properties at temperature
Substitute
Substitute
From the Table A-17, “Ideal-gas properties of air”.
Obtain the value of enthalpy at state 2
Write the formula of interpolation method of two variables.
Here, the variables denoted by x and y are relative pressure and enthalpy.
Show relative pressure and enthalpy values from the Table A-17.
Relative pressure | Enthalpy |
7.824 | 492.74 |
8.316 | ? |
8.411 | 503.02 |
Substitute
The value of enthalpy at state 2
Similarly by using interpolation method obtain the value of enthalpy at state 4
Substitute
Substitute
Substitute
Substitute
For relative pressure
Substitute
From the Table A-17, “Ideal-gas properties of air” obtain the values of enthalpy
Substitute
From the Table A-17, “Ideal-gas properties of air” obtain the values of enthalpy
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the change in net work output per unit mass is
b)
The change in thermal efficiency of the cycle.
Answer to Problem 164RP
The change in thermal efficiency of the cycle is
Explanation of Solution
Write the expression to calculate the change in thermal efficiency
Conclusion:
Substitute
Thus, the change in thermal efficiency of the cycle is
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