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 = 5.07 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 = 4.7°C, what is its temperature at the end of the adiabatic expansion?

Answer 1

Ratio of molar specific heats = $\gamma$ = 4/3

Initial pressure = P₁ = 5.07 atm

Initial temperature = T₁ = 4.7 ^oC = 277.7 K

Final pressure = P₂ = 1 atm

Final temperature = T₂

The process is specified to be adiabatic.

$P_{1}^{\frac{1-\gamma }{\gamma }}T_{1} = P_{2}^{\frac{1-\gamma }{\gamma }}T_{2}$

1-4/3 1-4/3 (5.07)--(277.7) = (1)T-T

T₂ = 185.06 K

T₂ = -87.94 ^oC

Temperature at the end of the adiabatic expansion = -87.94 ^oC