Question

In a diesel engine, the cylinder compresses air from approximately standard pressure and temperature to about one-sixteenth the original volume and a pressure of about 50 atm. The temperature of the compressed air is:

• A. 225 K
• B. 853 K
• C. 970 K
• D. 1043 K

Hint:

For adiabatic processes, use the adiabatic relation to determine changes in pressure, volume, and temperature.

Answer 1

The Correct Option is C

For an adiabatic compression process, we can use the adiabatic relation: \[ P V^\gamma = \text{constant} \] where \( P \) is the pressure, \( V \) is the volume, and \( \gamma \) is the adiabatic index (\( \gamma = 1.4 \) for air). Also, using the relation: \[ T_2 = T_1 \left( \frac{V_1}{V_2} \right)^{\gamma - 1} \] Since the volume is compressed to one-sixteenth of its original volume: \[ T_2 = T_1 \left( \frac{1}{16} \right)^{1.4 - 1} \approx 970 \, \text{K} \] Thus, the temperature of the compressed air is 970 K.