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# An air-standard Diesel cycle has a compression ratio of 18.2. Air is at $120^{\circ} \mathrm{F}$ and 14.7 psia at the beginning of the compression process and at 3200 R at the end of the heat-addition process. Determine the exergy destruction associated with the heat rejection process of the cycle, assuming a source temperature of 3200 R and a sink temperature of 540 R. Also, determine the exergy at the end of the isentropic expansion process. Account for the variation of specific heats with temperature.

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The relative specific volume, internal energy and entropy at state 1 are determined from A-17E for the given temperature:

\begin{align*} &u_{1}=98.9\:\dfrac{\text{Btu}}{\text{lbm}}\\ &s_{1}^{°}=0.61793\:\dfrac{\text{Btu}}{\text{lbm}\text{R}}\\ &\alpha_{r1}=120.7 \end{align*}

The relative specific volume at state 2 is determined from the compression ratio:

\begin{align*} \alpha_{r2}&=\dfrac{\alpha_{r1}}{r}\\ &=\dfrac{120.7}{18.2}\\ &=6.63 \end{align*}

The temperature at state 2 is determined from this value using interpolation with data from A-17E:

\begin{align*} T_{2}=1725.9\:\text{R} \end{align*}

The relative specific volume at state 4 is determined from the relative specific volume at state 3 taken from A-17E and the temperatures:

\begin{align*} \alpha_{r4}&=\dfrac{T_{2}}{T_{3}}r\alpha_{r3}\\ &=\dfrac{1725.9}{3200}\cdot18.2\cdot0.955\\ &=9.374 \end{align*}

From this value the internal energy, entropy and temperature at state 4 are determined from A-17E using interpolation:

\begin{align*} &u_{4}=272.59\:\dfrac{\text{Btu}}{\text{lbm}}\\ &s_{4}^{°}=0.85971\:\dfrac{\text{Btu}}{\text{lbm}\text{R}}\\ &T_{4}=1531.9\:\text{R} \end{align*}

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