## Related questions with answers

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.

Solution

VerifiedThe 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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