Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 58

Opening champagne. In a bottle of champagne, the pocket of gas (primarily carbon dioxide) between the liquid and the cork is at pressure of \( p_i = 5.00 \text{ atm} \). When the cork is pulled from the bottle, the gas undergoes an adiabatic expansion until its pressure matches the ambient air pressure of \( 1.00 \text{ atm} \). Assume that the ratio of the molar specific heats is \( \gamma = \frac{4}{3} \). If the gas has initial temperature \( T_i = 5.00^\circ\text{C} \), what is its temperature at the end of the adiabatic expansion?