An inflated balloon occupies a volume of two (2) liters. The balloon is tied with a string and weighted down with a heavy stone. What is its volume when it reaches the bottom of a pond 5.2 meters deep? Assume the atmospheric pressure is equal to 1 atmosphere and that one atmosphere will support a column of water 10.4 meters high.
P1V1=P2V2
P1 = 1 atm
P2=1atm(1+5.2/10.4)
V1=2liters
solve for V2
1.33?
a gas occupies a volume off 600cm3 at a given temperature. calculate the new vol. if the pressure is increased by5% and the temperarure is constant
To find the volume of the balloon when it reaches the bottom of the pond, we need to consider the change in pressure as it descends. The pressure increases as the depth increases.
Here's the step-by-step process to find the volume of the balloon at the bottom of the pond:
1. Determine the change in pressure between the surface and the bottom of the pond.
- The atmospheric pressure at the surface is 1 atmosphere.
- The pressure at the bottom of the pond is equal to the pressure due to the column of water above it, which is the atmospheric pressure plus the pressure due to the water depth. In this case, the depth is 5.2 meters, so the pressure at the bottom is 1 atmosphere + pressure due to the water column.
2. Calculate the pressure due to the water column.
- We know that one atmosphere supports a column of water 10.4 meters high, so the pressure due to the water column is the atmospheric pressure multiplied by the depth ratio.
- The depth ratio is the depth of the water column (5.2 meters) divided by the standard depth (10.4 meters).
- Therefore, the pressure due to the water column is 1 atmosphere × (5.2 meters / 10.4 meters).
3. Calculate the total pressure at the bottom of the pond.
- Add the atmospheric pressure to the pressure due to the water column to find the total pressure at the bottom of the pond.
4. Use the ideal gas law to find the volume of the balloon.
- We can rearrange the ideal gas law, PV = nRT, to solve for the volume (V).
- Since the number of moles (n), the gas constant (R), and the temperature (T) remain constant, we can write the equation as V₁/P₁ = V₂/P₂, where V₁ is the initial volume of the balloon, P₁ is the initial pressure (1 atmosphere), V₂ is the final volume we want to find, and P₂ is the final pressure at the bottom of the pond.
5. Substitute the values into the equation and solve for V₂.
- Plug in the values for V₁ and P₁ (2 liters and 1 atmosphere), and the value for P₂ calculated in step 3.
- Solve for V₂ to find the volume of the balloon at the bottom of the pond.
Following these steps will allow you to calculate the volume of the balloon at the bottom of the pond.