written 2.8 years ago by
Sharad
• 150


Given values:
 The initial temperature is $T_{1}=28^{\circ} \mathrm{C}$.
The initial pressure is $P_{1}=95 \mathrm{kPa}$.
The compression ratio is $r=18$.
The cutoff ratio is $r_{c}=2.2$.
Assumptions:
(1) The air standard assumptions are applicable.
(2) The kinetic and potential energy changes are negligible.
(3) Air is an ideal gas with variable specific heats.
The schematic diagram for the diesel cycle can be drawn as:
According to the ideal gas equation:
$$
P_{1} V_{1}=m R T_{1}
$$
Here, $R=287 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ is the universal gas constant for air and mass is $m=1 \mathrm{~kg}$. On rearranging the above equation, we get,
$$
V_{1}=\frac{m R T_{1}}{P_{1}}
$$
Substitute the values in the above equation.
$$
\begin{aligned}
V_{1} &=\frac{(1 \mathrm{~kg})(287 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K})\left[28^{\circ} \mathrm{C}+273\right] \mathrm{K}}{(95 \mathrm{kPa})\left(\frac{10^{3} \mathrm{~Pa}}{1 \mathrm{kPa}}\right)} \\
V_{1} & \approx 0.91 \mathrm{~m}^{3}
\end{aligned}
$$
Thus, the initial volume is $0.91 \mathrm{~m}^{3}$.