Volume of Bubble at Bottom of Lake: 1.00 cm3

[agadag]

Homework Statement

A bubble with a volume of 1.00 cm3 forms at the bottom of a lake that is 40 m deep. The temperature at the bottom of the lake is 10°C. The bubble rises to the surface where the water temperature is 31°C. Assume that the bubble is small enough that its temperature always matches that of its surroundings. What is the volume of the bubble just before it breaks the surface of the water? Ignore surface tension. Answer in cm3

Homework Equations

i wasn't sure how to go about solving this equation at all.
I know that : Change in V = k *V *change in Temp

PLEASE HELP!

 

[denverdoc]

At least you can ignore surface tension. The combined gas law is your best bet as temp and pressure are both changing. Recall that 1atm of pressure is equal to 10m of water. Be careful to include the regular barometric pressure at both the bottom and the surface.

 

[kerimek]

I would approach this problem by using the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

In this scenario, we can assume that the bubble is filled with air, which is a gas. We also know that the temperature of the bubble will remain constant at 10°C as it rises to the surface, since it is small enough to quickly reach thermal equilibrium with its surroundings.

Using the ideal gas law, we can rearrange the equation to solve for the number of moles of gas (n): n = PV/RT. We know the initial pressure, volume, and temperature of the bubble at the bottom of the lake, so we can plug those values in and solve for n.

Next, we can use the value of n to solve for the volume of the bubble at the surface, using the same equation and plugging in the new temperature of 31°C. This will give us the final volume of the bubble just before it breaks the surface of the water.

So in summary, the volume of the bubble just before it breaks the surface of the water can be calculated using the ideal gas law, taking into account the initial and final temperatures and the depth of the lake. This approach assumes that the bubble behaves as an ideal gas and that surface tension can be ignored.