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Air is compressed in an axialflow compressor operating at steady state from $27^{\circ} \mathrm{C},$ 1 bar to a pressure of 2.1 bar. The work required is 94.6 kJ per kg of air flowing. Heat transfer from the compressor occurs at an average surface temperature of $40^{\circ} \mathrm{C}$ at the rate of 14 kJ per kg of air flowing. The effects of motion and gravity can be ignored. Let $T_{0}=20^{\circ} \mathrm{C}, p_{0}=1$ bar. Assuming ideal gas behavior, (a) determine the temperature of the air at the exit, in $^\circ C,$ (b) determine the rate of exergy destruction within the compressor, in kJ per kg of air flowing, and (c) perform a full exergy accounting, in kJ per kg of air flowing, based on work input.
Solution
Verified$\rule{5in}{1pt}$
$\text{\textcolor{#4257b2}{\textbf{Given}}}$
For state 1:

The pressure $P_1 = 1 \ \mathrm{bar}$

The temperature $T_1 = 27 \ \mathrm{^\circ C}$

The pressure at state 2 $P_2 = 2.1 \ \mathrm{bar}$

The work required $\dfrac{\dot{W}_{cv}}{\dot{m}} = 94.6 \ \mathrm{\dfrac{kJ}{kg}}$

Heat transfer $\dfrac{\dot{Q}_{cv}}{\dot{m}} = 14 \ \mathrm{\dfrac{kJ}{kg}}$

Average surface temperature $T_b = 40 \ \mathrm{^\circ C}$
For reference state:

The pressure $P_0 = 1 \ \mathrm{bar}$

The temperature $T_0 = 20 \ \mathrm{^\circ C}$
$\text{\textcolor{#4257b2}{\textbf{Required}}}$
a)The temperature of the air at the exit in $[\ \mathrm{^\circ C}]$.
b)The rate of exergy destruction within the compressor in $\left[\ \mathrm{\dfrac{kJ}{kg}}\right]$ of air flowing.
c)full exergy accounting in $\left[\ \mathrm{\dfrac{kJ}{kg}}\right]$ of air flowing based on work input.
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