## Related questions with answers

A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at $800 \mathrm{~kPa}$ and $1100 \mathrm{~K}$ and leaves at $100 \mathrm{~kPa}$ and $670 \mathrm{~K}$. Heat is rejected to the surroundings at a rate of $6700 \mathrm{~kW}$, and air flows through the cycle at a rate of $18 \mathrm{~kg} / \mathrm{s}$. For what compressor efficiency will the gas-turbine power plant produce zero net work?

Solution

VerifiedZero net work is produced when the difference between the rate work between the inlet and outlet energies is zero.

$\begin{gather*} \dot{W}_{\mathrm{net}, \text { out }}= \dot{W}_{\mathrm{C}, \text { in }}-\dot{W}_{\mathrm{T}, \mathrm{out}} \\ 0 = \dot{W}_{\mathrm{C}, \text { in }}-\dot{W}_{\mathrm{T}, \mathrm{out}}\\ \dot{W}_{\mathrm{C}, \text { in }} = \dot{W}_{\mathrm{T}, \mathrm{out}} \end{gather*}$

Where $\dot{W}_{\mathrm{C}, \text { in }}$ is

$\dot{W}_{\mathrm{C}, \mathrm{in}}=\dot{m}\left(h_{2 s}-h_{1}\right) / \eta_{C}$

and $\dot{W}_{\mathrm{T}, \mathrm{out}}$ is

$\dot{W}_{\mathrm{T}, \mathrm{out}}= \dot{m}\left(h_{3}-h_{4}\right)$

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