Question

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 = 2.98 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 atm. Assume that the ratio of the molar specific heats is γ = 4/3. If the gas has initial temperature T = 2.6°C, what is its temperature at the end of the adiabatic expansion?

Answer 1

Let p, V, and T, represent the pressure, volume, and temperature of the initial state of the gas, and let p, V, and T be the pressure, volume, and temperature of the final state. Since the process is adiabatic p p Combining with the ideal gas law, pr = NRT , we obtain With y-4/3, which gives (1-y)/y--1/4, the temperature at the end of the adiabatic expansion is T, I 298 atm)-1/4 1.00 atm) Pi (275.6 K)-209.7K--63°C Ps

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