Answer :
Final answer:
When an ideal gas is compressed adiabatically, the relationship between the volume and temperature can be described using an equation. By plugging in the given values and solving the equation, we find that the rise in temperature is 81 degrees Celsius.
Explanation:
When an ideal gas is compressed adiabatically (without gaining or losing heat), the relationship between the volume and temperature can be described using the equation:
T₁ × V₁^(γ-1) = T₂ × V₂^(γ-1)
Where T₁ and V₁ are the initial temperature and volume, T₂ and V₂ are the final temperature and volume, and γ is the specific heat ratio (5/3 for this gas).
In this case, the initial temperature is 27°C (300 K), the volume is compressed to 8/27 of its original volume, and γ is 5/3. Plugging in these values into the equation gives:
300 K × 1^(5/3-1) = T₂ × (8/27)^(5/3-1)
Simplifying the equation gives:
T₂ = 81 K
Therefore, the rise in temperature is 81 K, which is equivalent to 81 degrees Celsius. So, the correct answer is option a) 81 degrees Celsius.
