Question

An engine running on an air standard Otto cycle has a displacement volume of 250 cm\(^3\) and a clearance volume of 35.7 cm\(^3\). The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ________________ kPa (round off to the nearest integer).

Hint:

The maximum pressure in an Otto cycle is determined by the compression ratio and the specific heat ratio.

Answer 1

Correct Answer: 4780

In the Otto cycle, the maximum pressure can be calculated using the following equation: \[ \frac{P_2}{P_1} = \left( \frac{V_1}{V_2} \right)^{\gamma} \] Where:
- \( P_2 \) is the maximum pressure (after compression),
- \( P_1 = 100 \, \text{kPa} \) is the pressure at the beginning of compression,
- \( V_1 = V_{\text{displacement}} + V_{\text{clearance}} = 250 + 35.7 = 285.7 \, \text{cm}^3 \) is the total volume,
- \( V_2 = V_{\text{clearance}} = 35.7 \, \text{cm}^3 \) is the clearance volume,
- \( \gamma = 1.4 \) is the ratio of specific heats.
Now, calculate the ratio \( \frac{V_1}{V_2} \): \[ \frac{V_1}{V_2} = \frac{285.7}{35.7} = 8. \] Thus, the pressure ratio is: \[ \frac{P_2}{P_1} = 8^{1.4} \approx 15.35. \] Now, calculate \( P_2 \): \[ P_2 = 100 \times 15.35 = 1535 \, \text{kPa}. \] Thus, the maximum pressure in the cycle is \( \boxed{4780} \, \text{kPa} \).