Final answer:
To calculate the change in rainwater level, we need to find the difference in the initial and final volumes of the gas-filled balloon. Given that the balloon provides enough lift for a 41.7 g package, we can calculate the volume of the gas using the ideal gas law. Once we have the mass of the gas, we can use the density of water to find the change in rainwater level.
Step-by-step explanation:
To calculate the change in rainwater level, we need to find the difference in the initial and final volumes of the gas-filled balloon. Given that the balloon provides enough lift for a 41.7 g package, we can calculate the volume of the gas using the ideal gas law, V = nRT/P. The mass of the gas can be calculated as the difference between the mass of the package and the mass of the empty balloon. Once we have the mass of the gas, we can use the density of water to find the change in rainwater level.
First, calculate the volume of the gas in the balloon using the ideal gas law. Rearrange the equation to solve for volume:
V = (nRT) / P
Where:
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant (8.31 J/(mol·K))
- T is the temperature in Kelvin
- P is the pressure
Using the given information, plug in the values and calculate the volume of the gas. Next, calculate the mass of the gas by subtracting the mass of the empty balloon from the mass of the package. Then, use the density of water (1000 kg/m³) to find the change in rainwater level using the formula:
Change in rainwater level = mass of the gas / (density of water * cross-sectional area of the balloon)
Plug in the values and calculate the change in rainwater level.