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A perfect gas at 1 bar and 290 K undergoes ideal diesel cycle.

The maximum pressure of the cycle is 50 bar. The volume at the beginning of compression is 1 $m^3$ and after constant pressure heating is 0.1 $m^3$. Determine the temperature at all salient points of the cycle and also find out the efficiency of the cycle. Take γ=1.4 for the gas.

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T1 = 290 K

For isentropic compression 1-2

$\frac{T2}{T1} = \big(\frac{p2}{p1}\big)^{\frac{γ-1}{γ}} \hspace{0.9cm} ∴ \frac{T2}{290} = \big(\frac{50}{1}\big)^{\frac{1.4-1}{1.4}} **∴T2=886.78** K$

$\frac{p1v1}{T1} = \frac{p2v2}{T2} \hspace{0.9cm} ∴ \frac{1×1}{290} = \frac{50×v2}{886.78} ∴ v2 = 0.0612 m3$

Since $p2=p3 \frac{v2}{T2} = \frac{v3}{T3} \hspace{0.9cm} ∴ T3=1448.98 K $

For isentropic expansion 3-4

$\frac{T4}{T3} = \Big(\frac{v3}{v4}\Big)^{γ-1} \hspace{0.9cm} ∴ …

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