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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.

1 Answer

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Final answer:

To determine the change in the net work output per unit mass and the thermal efficiency of a simple ideal Brayton cycle with air as the working fluid, the net work output and thermal efficiency formulas need to be used and the new temperatures and pressures calculated.

Step-by-step explanation:

To determine the change in the net work output per unit mass and the thermal efficiency of a simple ideal Brayton cycle with air as the working fluid, we first need to understand the Brayton cycle and its components. The Brayton cycle is a thermodynamic cycle that consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection. In this case, the pressure ratio of the cycle is doubled without changing the minimum and maximum temperatures.

(a) The net work output per unit mass for the Brayton cycle can be calculated using the equation:

Net work = Cp(T3 - T4) - Cp(T2 - T1)

Where T1 is the initial temperature, T2 is the temperature after compression, T3 is the temperature after heat addition, and T4 is the temperature after expansion. Cp represents the specific heat at constant pressure of the working fluid (air). By doubling the pressure ratio, the new temperatures can be calculated, and the change in net work output per unit mass can be determined.

(b) The thermal efficiency of the Brayton cycle can be calculated using the equation:

Thermal efficiency = 1 - (1 / pressure ratio)((k - 1) / k)

Where k is the ratio of specific heats (Cp/Cv) of the working fluid (air). By doubling the pressure ratio, the new thermal efficiency can be calculated.

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