To find the initial temperature of the balloon, we can use the ideal gas law, which states:
PV = nRT
Where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature
Assuming the pressure remains constant, we can rearrange the equation to solve for temperature:
T = PV / (nR)
Since the number of moles (n) and the ideal gas constant (R) remain constant, we can simplify the equation to:
T = kV
Where k is a constant.
Let's denote the initial temperature as T1 and the initial volume as V1. We have the following information:
T1 = ? V1 = 200 ml T2 = 33°C V2 = 120 ml
We can set up a ratio of temperatures and volumes:
T1 / V1 = T2 / V2
Substituting the known values:
T1 / 200 ml = 33°C / 120 ml
Simplifying:
T1 = (33°C / 120 ml) * 200 ml T1 = (33°C * 200) / 120 T1 = 55°C
Therefore, the initial temperature of the 200 ml balloon is 55°C.