To determine the temperature to which a 2.3L balloon must be heated in order to expand to a volume of 4001L, we can use Charles' Law. Charles' Law states that, at constant pressure, the volume of a gas is directly proportional to its temperature.
The equation for Charles' Law can be written as:
V₁ / T₁ = V₂ / T₂
where V₁ and T₁ represent the initial volume and temperature of the balloon, respectively, and V₂ and T₂ represent the final volume and temperature.
Let's plug in the known values into the equation:
V₁ = 2.3L T₁ = 25°C = 298K (converted to Kelvin)
V₂ = 4001L (the desired final volume)
Now we can solve for T₂ (the final temperature):
T₂ = (V₂ * T₁) / V₁ = (4001L * 298K) / 2.3L ≈ 518,304K
Therefore, the balloon would need to be heated to approximately 518,304 Kelvin (or 518,031 degrees Celsius) in order to expand from 2.3L to 4001L, assuming constant pressure and starting at an initial temperature of 25°C (298K).