Answer: To calculate the temperature to which the gas must be raised to double the volume of the balloon, we can use Charles's Law, which states that the volume of a given amount of gas at a constant pressure is directly proportional to its absolute temperature. The equation for Charles's Law is:
V1 / T1 = V2 / T2
where:
V1 = initial volume of the gas (before doubling, in any units)
T1 = initial temperature of the gas (in Kelvin)
V2 = final volume of the gas (after doubling, in the same units as V1)
T2 = final temperature of the gas (in Kelvin)
We want to find T2, so let's rearrange the equation:
T2 = (V2 * T1) / V1
Given:
T1 = 12.5 °C + 273.15 K (convert to Kelvin)
V2 = 2 * V1 (since we want to double the volume)
Now, plug in the values:
T2 = (2 * V1 * T1) / V1
The initial volume (V1) cancels out, and we are left with:
T2 = 2 * T1
Now, calculate T2:
T2 = 2 * (12.5 °C + 273.15 K)
Now, convert back to Celsius if needed:
T2 ≈ 2 * 285.65 K ≈ 571.3 K
Now, convert the temperature to Celsius:
T2 ≈ 571.3 K - 273.15 ≈ 298.15 °C
So, the temperature of the gas must be raised to approximately 298.15 °C in order to double the volume of the balloon.