To determine the new volume of the balloon when the temperature drops from 39°C to 8°C, we can use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where: P = pressure (assumed constant) V = volume n = number of moles of gas (assumed constant) R = ideal gas constant T = temperature
Since the number of moles of gas and pressure are assumed to be constant, we can simplify the equation to:
V1/T1 = V2/T2
where: V1 = initial volume of the balloon T1 = initial temperature V2 = new volume of the balloon (to be calculated) T2 = new temperature
Plugging in the given values: V1 = 1.28 L T1 = 39°C + 273.15 (converted to Kelvin) = 312.15 K T2 = 8°C + 273.15 (converted to Kelvin) = 281.15 K
Using the equation, we can solve for V2:
V1/T1 = V2/T2
1.28 L / 312.15 K = V2 / 281.15 K
V2 = (1.28 L * 281.15 K) / 312.15 K
V2 ≈ 1.152 L
Therefore, when the temperature drops from 39°C to 8°C, the new volume of the balloon would be approximately 1.152 L.