Final answer:
An ideal monatomic gas undergoes adiabatic expansion and its final temperature can be calculated using the equation 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 225 K. The correct answer is option C.
Step-by-step explanation:
An adiabatic process is one in which there is no heat transfer to or from the gas. In this case, an ideal monatomic gas expands adiabatically and reversibly to twice its volume. During the adiabatic expansion, the temperature of the gas decreases.
The relationship between the initial and final temperatures and volumes for an adiabatic process can be described by the equation T₁V₁^(γ-1) = T₂V₂^(γ-1), where γ is the heat capacity ratio, which is equal to 5/3 for a monatomic gas.
Using this equation, we can find the final temperature T₂:
T₂ = T₁(V₁/V₂)^(γ-1)
Plugging in the values T₁ = 300 K and V₁/V₂ = 2, we get:
T₂ = 300 K * (1/2)^(5/3) = 225 K
Therefore, the final temperature of the gas is 225 K.