Question

Air in an ideal Diesel cycle is compressed from 3 litre to 0.15 litre. It then expands during a constant pressure heat addition process to 0.3 litre. If the ratio of specific heats, \( \gamma = 1.4 \), the thermal efficiency (in %) of the cycle is ........ (rounded to one decimal place).

Hint:

For an ideal Diesel cycle, the thermal efficiency increases with the compression ratio. Higher compression ratios lead to more efficient cycles, but the cycle's maximum temperature also rises.

Answer 1

The thermal efficiency \( \eta \) of an ideal Diesel cycle can be calculated using the formula for thermal efficiency for an idealized engine cycle: \[ \eta = 1 - \frac{1}{r^{\gamma - 1}} \] where \( r \) is the compression ratio and \( \gamma \) is the ratio of specific heats. First, calculate the compression ratio \( r \): \[ r = \frac{V_1}{V_2} = \frac{3 \, {litres}}{0.15 \, {litres}} = 20 \] Now, substitute the values into the efficiency formula: \[ \eta = 1 - \frac{1}{20^{1.4 - 1}} = 1 - \frac{1}{20^{0.4}} \approx 1 - \frac{1}{2.639} \approx 1 - 0.379 \approx 0.621 \] Thus, the thermal efficiency of the Diesel cycle is approximately \( 62.1% \), which lies between 63 and 66%.