Pressure, Volume & Temperature: Homework Solutions

In summary, the question asks for the new pressure in a 12 litre gas bottle filled with air at 232 BAR and 30 C, once it has cooled to 8 C. For the second part, a diver breathing from the bottle at a depth of 40m and a temperature of 8 C, is asked to determine the volume of a bubble of exhaled air at the surface. Using the combined gas law, the pressure at 40m is calculated to be 492800 Pa. The pressure at the surface is given as 100'000 Pa. However, the calculated volume of the bubble at the surface is incorrect and further calculations are needed.
  • #1
ar202
45
0

Homework Statement



A 12 litre gas bottle is initially charged with air to 232 BAR at 30 C. What will be the new pressure in the bottle once it has cooled to 8 C?

A diver breathes from the gas bottle above, is working at a depth of 40m, and at a temperature of 8 C.

If the diver exhales a bubble of air with a volume of 0.5 litres, what will the volume of the bubble be when it reaches the surface?

Homework Equations



not sure...

The Attempt at a Solution



I know for the first part that using the combined gas law

(P1/T1) x T2 = 215 BAR

P = pressure
T = temperature in kelvin

However I'm stuck on where to go with the next part.

Any pointers/hints in the right direction would be really appreciated. thanks
 
Physics news on Phys.org
  • #2
Since you know the diver's depth you can determine the pressure at that depth. You are also given the temperature and volume of the air bubble at that depth. As the bubble rises it will expand to a larger volume. You will need to determine a pressure and temperature at the surface to find the new volume.
 
  • #3
Have ended up with the volume of the bubble at surface = 2.2L

anyone think this is correct?
 
  • #4
ar202 said:
Have ended up with the volume of the bubble at surface = 2.2L

anyone think this is correct?

Not me.

What is a pressure at 40 meters? What is a pressure at the surface?
 
  • #5
Pressure at 40m = 1000(p) x 9.81(g) x 40(h) + Atmospheric pressure (100'000) = 492800

Pressure at surface = 100'000 Pa

...
 

1. What is the Ideal Gas Law and how is it used to solve problems related to pressure, volume, and temperature?

The Ideal Gas Law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of an ideal gas. It is written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. This equation can be used to solve for any of the variables, as long as the others are known. It is particularly useful in solving problems related to gas behavior, such as predicting the volume of a gas at a certain pressure and temperature, or determining the temperature at which a gas will reach a certain pressure.

2. How does changing the temperature affect the pressure of a gas?

According to Charles' Law, the volume of a gas is directly proportional to its temperature, as long as the pressure and number of moles of gas remain constant. This means that as the temperature of a gas increases, its volume increases, and therefore its pressure also increases. This is because as the gas particles gain more energy and move faster, they collide with the walls of their container more frequently, resulting in a higher pressure.

3. Can you explain the relationship between pressure and volume in Boyle's Law?

Boyle's Law states that the pressure of a gas is inversely proportional to its volume, as long as the temperature and number of moles of gas remain constant. This means that as the volume of a gas decreases, its pressure increases, and vice versa. This is because when the volume of a gas is decreased, the same number of gas particles are present in a smaller space, resulting in more frequent collisions with the walls of the container and a higher pressure.

4. How is the Combined Gas Law used to solve problems involving pressure, volume, and temperature?

The Combined Gas Law combines the three individual gas laws (Boyle's Law, Charles' Law, and Gay-Lussac's Law) into one equation that can be used to solve for any of the variables as long as the others are known. It is written as P1V1/T1 = P2V2/T2, where P1 and V1 are the initial pressure and volume, T1 is the initial temperature, P2 and V2 are the final pressure and volume, and T2 is the final temperature. This equation is particularly useful in solving problems where two variables are changing simultaneously, such as when a gas is heated and its volume and pressure both change.

5. How do real gases differ from ideal gases and how does this affect the calculations for pressure, volume, and temperature?

Real gases behave differently than ideal gases, particularly at high pressures and low temperatures. Unlike ideal gases, real gases have volume and attractive forces between particles, which can affect their behavior. This means that the Ideal Gas Law and other gas laws may not be accurate for real gases under certain conditions. In these cases, more complex equations, such as the van der Waals equation, may need to be used to calculate pressure, volume, and temperature. Additionally, real gases may exhibit deviations from the ideal gas law, so experimental data may be needed to obtain more accurate values for these variables.

Similar threads

Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
    • Introductory Physics Homework Help
Replies
8
Views
744
Gas temperature in a constant volume
    • Introductory Physics Homework Help
Replies
8
Views
913
A water-bottle demonstration of atmospheric pressure
    • Introductory Physics Homework Help
Replies
6
Views
319
Why does the pressure of a gas bubble change as it rises?
    • Introductory Physics Homework Help
Replies
4
Views
1K
Find volume of pesticide after pressure decreases
    • Introductory Physics Homework Help
Replies
3
Views
796
Thermal physics problem -- Pressure and temperature of air in a refrigerator
    • Introductory Physics Homework Help
Replies
2
Views
4K
Calculate the ratio of new volume to old volume
    • Introductory Physics Homework Help
Replies
2
Views
2K
Engineering Calculating the mass of air in a pressurised air tank
    • Engineering and Comp Sci Homework Help
Replies
14
Views
1K
Pressure Half-Life: 2L vs. 5L Containers
    • Introductory Physics Homework Help
Replies
1
Views
1K
Pressurized gas container gets opened
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top