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# An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and $27^{\circ} \mathrm{C}$. Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure.

Solution

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First the internal energy and relative specific volume at state 1 are determined from the given temperature and data from A-17:

\begin{align*} &u_{1}=214.07\:\dfrac{\text{kJ}}{\text{kg}}\\ &\alpha_{r1}=621.2 \end{align*}

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

\begin{align*} \alpha_{r2}&=\dfrac{\alpha_{r1}}{r}\\ &=\dfrac{621.2}{16}\\ &=38.825 \end{align*}

The enthalpy and temperature at this state can be determined from this value with data from A-17 using interpolation:

\begin{align*} &h_{2}=890.89\:\dfrac{\text{kJ}}{\text{kg}}\\ &T_{2}=862.4\:\text{K} \end{align*}

The temperature at state 3 is determined from the cutoff ratio:

\begin{align*} T_{3}&=T_{2}r_{c}\\ &=862.4\cdot2\:\text{K}\\ &=\boxed{1724.8\:\text{K}} \end{align*}

From this the enthalpy and relative specific volume at this state are determined with data from A-17 using interpolation:

\begin{align*} &h_{3}=1910.6\:\dfrac{\text{kJ}}{\text{kg}}\\ &\alpha_{r3}=4.546 \end{align*}

The relative specific volume at state 4 can be determined from the compression and cutoff ratio:

\begin{align*} \alpha_{r4}&=\dfrac{r}{r_{c}}\alpha_{3}\\ &=\dfrac{16}{2}\cdot4.546\\ &=36.37 \end{align*}

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