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Standard XII

Physics

Area and Volume Expansion

Helium is use...

Question

Helium is used as the working fluid in an ideal brayton cycle. The gas enters at $27^{\circ} C, 20$ bar pressure. The gas is heated to $1000^{\circ} C, 60$ bar pressure before entering the turbine. The cooler returns the hot turbine exhaust to the temperature of the comressor inlet. Take $(C_{p}) Helium = 5.1926 k J / k g K$ . The net work for 2 kg of helium is ____ kJ.
2982.6

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Solution

The correct option is A 2982.6

$γ = 1.66$

$(C_{p}) = 5.1926 k J / k g K$

$T_{1} = 27^{\circ} C = 300 K$

$T_{2} = T_{1} (\frac{P_{2}}{P_{1}}) γ - 1 / γ = 300 {(\frac{60}{20})}^{1.66 - 1 / 1.66} = 464.32 K$

$T_{3} = 1000^{\circ} C = 1273 K$

$T_{4} = \frac{T_{3}}{(P_{3} / P_{4})^{γ - 1 / γ}} = \frac{1273}{(3)^{0.66 / 1.66}} = 822.4 K$

$W_{net} = W_{T} - W_{C}$

$= m c_{p} (T_{3} - T_{4}) - m c_{p} (T_{2} - T_{1})$

$= 2 \times 5.1926 (1273 - - 822.4) - 2 \times 5.1926 (464.32 - 300)$

$= 2972.16 k J$

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