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sawhai

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## Homework Statement

A gas turbine power plant operates on the regenerative Brayton cycle as shown in the figure.

Compression occurs in two stages, with interstage cooling, and expansion in the turbine

likewise occurs in two stages, with interstage reheating. The cycle operates between the

pressure limits of P1 = P9 = P10 = 100 kPa and P4 = P5 = P6 = 1200 kPa.

Interstage cooling/heating occur at the thermodynamic optimum P2 = P3 = P7 = P8 = 346.4 kPa(i.e. the geometric mean of the intake air and combustor pressures). Air enters each

compression stage at T1 = T3 = 300 K. Combustion gases enter the first and second stages of

the turbine at T6 = 1400 K and T8 = 1300 K respectively. The compressor and the turbine both

have an isentropic efficiency of 80%. The regenerator has an effectiveness of 75%; i.e.

εregen = (h9 – h10)/(h9 – h4) = 0.75.

Assuming that the gas power cycle can be modeled using the air standard assumptions, with

variable (i.e. temperature-dependent) specific heats for air, and an air mass flow rate

m = 90 kg/s, determine the following:

(a). The net work output Wnet (MW) for the cycle.

(b). The back work ratio rbw; i.e. the fraction of the turbine work output that is used to drive

the compressor.

(c). The water supply rate, mW (kg/s), needed for interstage cooling in the compressor, if

liquid water at ambient temperature (300 K) is sprayed into the air between the two

compressor stages to provide evaporative cooling.

(d). The second-law efficiency η II = η th /η max for this gas turbine cycle; i.e. the ratio of the actual thermal efficiency to the maximum possible (Carnot) efficiency.

## Homework Equations

Ein = Eout

## The Attempt at a Solution

Parts a & b are done. I have done all the analysis across the power plant and have found all the temperatures in each stage (1-10). I have two questions:

1- It mentions in problem statement that the air has variable specific heat, does it mean that I have to use different values for the specific heat in each stage like compressor, coolant, etc. depending on the temperature in that stage?

2- For part C, how can I find the water supply rate in interstage cooling?

Thank you