Opening champagne. In a bottle of champagne, the pocket of gas (primarily carbon dioxide) between the liquid and the cork is al pressure of `p_i` = 4.00 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 `gamma`= 4/3. If the gas has initial temperature `T=5.00^@ C`, what is its temperature at the end of the adiabatic expansion?

Explanation

To solve the problem of finding the final temperature of the gas after adiabatic expansion when the cork is pulled from a champagne bottle, we can follow these steps:

### Step 1: Understand the Given Data
- Initial pressure, \( P_1 = 4.00 \, \text{atm} \)
- Final pressure, \( P_2 = 1.00 \, \text{atm} \)
- Initial temperature, \( T_1 = 5.00 \, ^\circ C \)
- Ratio of specific heats, \( \gamma = \frac{4}{3} \)

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