To calculate the required temperature for a balloon to expand to a specific volume, we need to use the ideal gas law, which states:
PV = nRT
Where: P = pressure of the gas V = volume of the gas n = number of moles of the gas R = ideal gas constant T = temperature in Kelvin
In this case, we assume the pressure (P) remains constant, so we can simplify the equation to:
V1/T1 = V2/T2
Where: V1 = initial volume of the balloon T1 = initial temperature of the balloon V2 = final volume of the balloon T2 = final temperature of the balloon
Given: V1 = 2.3 L T1 = 25 °C = 298.15 K (converting to Kelvin) V2 = 400 L
Let's calculate T2:
V1/T1 = V2/T2
T2 = (V2 * T1) / V1 = (400 * 298.15) / 2.3 ≈ 51758.26 K
Therefore, the balloon would have to reach a temperature of approximately 51758.26 Kelvin to expand to a volume of 400 L, assuming the initial temperature is 25 °C.