Final answer:
The final temperature after an adiabatic and reversible expansion can be calculated using the formula T2 = T1 * (V1/V2)^(γ-1), where T1 is the initial temperature, V1 is the initial volume, V2 is the final volume, and γ is the heat capacity ratio. In this case, the final temperature is approximately 238 K.
Step-by-step explanation:
In order to determine the final temperature after an adiabatic and reversible expansion, we can use the formula:
T2 = T1 * (V1/V2)^(γ-1)
Where T2 is the final temperature, T1 is the initial temperature (300 K in this case), V1 is the initial volume, V2 is the final volume (twice the initial volume), and γ is the heat capacity ratio for a monatomic gas (5/3 for an ideal monatomic gas).
Plugging in the values:
T2 = 300 K * (1/2)^(5/3-1) = 300 K * (1/2)^(2/3) = 300 K * 0.7937 ≈ 238 K