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Carnot Cycle

The schematic...

Question

The schematic of a two stage air compressor with an intercooler is shown.

The temperature of air after first stage compression is _____°C. (Assume all process to be ideal and optimal)
157.94

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Solution

The correct option is A 157.94

Since intercooling is optimal.

$P_{2} = \sqrt{P_{1} P_{4}} = \sqrt{100 \times 1600} = 400 k P a$

Also compression in compressor 1 is reversible and adiabatic.

$∴ T_{2} = T_{1} {(\frac{P_{2}}{P_{1}})}^{γ - 1 / γ} = 290 \times {(\frac{400}{100})}^{0.4 / 1.4} = 430.94 K$

$T_{2} = {157.94}^{\circ} C$

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