Question

An air-standard Diesel cycle with a compression ratio of 16 takes air at 1 bar and 300 K. If the maximum temperature in the cycle is 2100 K, then the thermal efficiency of the cycle is \(\underline{\hspace{2cm}}\) % (1 decimal place). 
The ratio of the specific heat capacities of air is 1.4.

Hint:

To calculate the thermal efficiency of a Diesel cycle, use the compression ratio and the ratio of specific heats in the efficiency formula.

Answer 1

Correct Answer: 59

For the Diesel cycle, the thermal efficiency \( \eta \) is given by the equation:
\[ \eta = 1 - \left( \frac{1}{r^{(\gamma - 1)}} \right) \] where:
\( r \) is the compression ratio, and
\( \gamma = 1.4 \) is the ratio of the specific heat capacities of air.
Given that the compression ratio is \( r = 16 \) and \( \gamma = 1.4 \), we can substitute these values into the equation:
\[ \eta = 1 - \left( \frac{1}{16^{(1.4 - 1)}} \right) \] \[ \eta = 1 - \left( \frac{1}{16^{0.4}} \right) \] \[ \eta = 1 - \left( \frac{1}{2.639} \right) \] \[ \eta = 1 - 0.379 \] \[ \eta = 0.621 \] The thermal efficiency is \( 62.1% \).