Air in an engine cylinder is quickly compressed from an initial temperature of 10 $\circ$ C,an initial pressure of 1.0 atmosphere,and an initial volume of 250 cm³ to a final volume of 30 cm³.Assuming the air to be an ideal diatomic gas,find the final temperature of the air.

Question

Quizplus · Accepted Answer

To find the final temperature of the air in the engine cylinder, we can use the ideal gas law and the concept of adiabatic compression. For an adiabatic process involving an ideal diatomic gas, the equation relating the initial and final states is $T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{\gamma-1}$, where $\gamma = \frac{C_p}{C_v} = \frac{7}{5}$ for a diatomic gas. Given $T_1 = 10^\circ C = 283 K$, $V_1 = 250 \, \text{cm}^3$, and $V_2 = 30 \, \text{cm}^3$, we can calculate $T_2$. Converting the final temperature back to Celsius gives a result close to 390°C, indicating that choice B is correct.

Air in an Engine Cylinder Is Quickly Compressed from an Initial