Final answer:
Applying the principle of conservation of energy to two bodies of O₂ with different initial temperatures, the final temperature of the mixture is found to be 33°C. This result is based on the fact that the heat gained by the cooler oxygen is equal to the heat lost by the warmer oxygen, leading them to reach thermal equilibrium.
Step-by-step explanation:
The question at hand involves the concept of thermal equilibrium. When two bodies with different temperatures are mixed in a thermally isolated system (no heat exchange with the surroundings), they will eventually reach a common final temperature. We can determine this final temperature by applying the principle of conservation of energy, specifically the heat gained or lost by one body is equal to the heat lost or gained by the other.
Since both bodies are oxygen (O₂), they have the same specific heat capacity. The mass and initial temperatures are given, but since both samples are at constant volume and there is no heat lost to the surroundings, we can use the equation: m1 × c × (Θf - Θi1) = m2 × c × (Θi2 - Θf), where m1 and m2 are the masses, c is the specific heat capacity, Θi1 and Θi2 are initial temperatures, and Θf is the final temperature. Since c is a constant and appears on both sides of the equation, it cancels out.
Let's solve for the final temperature Θf:
12 g × (30°C − Θf) = 6 g × (Θf − 39°C)
Θf = (12 g × 30°C + 6 g × 39°C) / (12 g + 6 g)
Θf = (360 + 234) / 18
Θf = 594 / 18
Θf = 33°C
Thus, the correct answer is none of the given options, as the final temperature of the mixture is 33°C.