## Related questions with answers

A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle $(\varepsilon=100$ percent) with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 880 kPa and 1100 K. Heat is transferred to air from an external source at a rate of 30,000 kJ/s. Determine the power delivered by this plant (a) assuming constant specific heats for air at room temperature and (b) accounting for the variation of specific heats with temperature.

Solution

Verified$\textbf{\large Part A}$

In this case the power is determined from the given rate of heat input and the efficiency relation:

$\begin{align*} \dot W&=\eta\dot Q_{\text{in}}\\ &=\bigg(1-\dfrac{T_{1}}{T_{3}}r_{p}^{(k-1)/k}\bigg)\dot Q_{\text{in}}\\ &=\bigg(1-\dfrac{290}{1100}\bigg(\dfrac{880}{95}\bigg)^{(1.4-1)/1.4}\bigg)\cdot30000\:\text{kW}\\ &=\boxed{15060\:\text{kW}} \end{align*}$

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