Answer: To calculate the volume of the balloon when the temperature of the air inside is raised, we can use the ideal gas law, which states:
PV = nRT
where:
P = pressure of the gas (assuming constant)
V = volume of the gas
n = number of moles of gas (assuming constant)
R = ideal gas constant (8.314 J/(mol*K))
T = temperature of the gas in Kelvin
Since the number of moles of gas and the pressure remain constant, we can use the relationship between the initial and final volumes and temperatures:
(V1 / T1) = (V2 / T2)
where:
V1 = initial volume of the balloon (117.5 m³)
T1 = initial temperature of the air inside the balloon (10.6 °C + 273.15 K)
V2 = final volume of the balloon (unknown)
T2 = final temperature of the air inside the balloon (45.0 °C + 273.15 K)
Now, let's plug in the values and solve for V2:
(V1 / T1) = (V2 / T2)
V2 = (V1 * T2) / T1
V2 = (117.5 m³ * (45.0 °C + 273.15 K)) / (10.6 °C + 273.15 K)
Now, let's convert all temperatures to Kelvin:
T1 = 10.6 °C + 273.15 K ≈ 283.75 K
T2 = 45.0 °C + 273.15 K ≈ 318.15 K
Now, calculate V2:
V2 = (117.5 m³ * 318.15 K) / 283.75 K
V2 ≈ 131.96 m³
So, the volume of the balloon when the temperature of the air inside is raised to 45.0 °C will be approximately 131.96 m³.