Pressure/Volume change

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These two questions are somewhat related, since the temperature affects the pressure.In summary, the problem involves raising the pressure in a volume from 16 PSI to 40 PSI using a second tank with a maximum pressure of 100 PSI. The volume of the second tank needs to be calculated. To solve this, you would use the ideal gas law and consider the relationship between pressure and volume. However, there is some ambiguity in the problem regarding the gas being released and the temperature remaining constant.
  • #1
pavadrin
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Homework Statement


The pressure in a volume of 1760 cubic inches needs to be raised from 16PSI to 40PSI. This is done via a second tank which has a maximum pressure of 100PSI. In order for this system to function, the second volume needs to be of a certain size. Calculate the volume required for tank.


Homework Equations


Not sure.


The Attempt at a Solution


I am stuck on how I can use PSI which is a measurement of pressure for an area with volume.
Any suggestions on where I could start would be greatly appreciated, as I am truly stuck.

Many thanks,
pavadrin
 
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  • #2
You would use the pressure in the ideal gas law. The unit, PSI, is pounds per square inch; one atmosphere pressure is close to 14.7 PSI. (Pressure always has units which involve area, since it is defined as the force per area on a surface.)

The problem is a bit unclear on one point. Is the gas in the second tank going to be released into the first volume, so that it mixes with it to raise the pressure? Is it assumed that the temperature remains constant while this happens?
 
  • #3


I would suggest starting by using the ideal gas law, which relates pressure, volume, and temperature. The equation is 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. Since the temperature is constant in this scenario, we can rearrange the equation to solve for volume: V = (nRT)/P.

In this problem, we are given the initial volume (1760 cubic inches), initial pressure (16 PSI), and final pressure (40 PSI). We can also assume that the number of moles of gas and the gas constant are constant. Therefore, we can set up a proportion using the ideal gas law:

(1760 cubic inches)/16 PSI = (x cubic inches)/40 PSI

Solving for x, we get x = (1760 cubic inches)(40 PSI)/16 PSI = 4400 cubic inches.

So, the required volume for the second tank is 4400 cubic inches. This is assuming that the gas in the second tank is the same as the gas in the first tank and that the temperature remains constant. If these assumptions are not true, then the calculation may be more complex.
 

1. How does pressure affect volume?

According to Boyle's Law, pressure and volume have an inverse relationship. This means that as pressure increases, volume decreases, and vice versa. This is because when pressure is applied to a gas, the molecules are forced closer together, resulting in a decrease in volume.

2. What is the formula for calculating pressure?

The formula for calculating pressure is P = F/A, where P is pressure, F is force, and A is the area over which the force is applied. The SI unit for pressure is Pascal (Pa) and is typically expressed in units of kilopascals (kPa) or atmospheres (atm).

3. How does changing the volume of a gas affect its pressure?

According to Charles's Law, volume and pressure have a direct relationship. This means that as the volume of a gas increases, the pressure also increases, and vice versa. This is because as the volume of a gas increases, the molecules have more space to move around, resulting in more collisions and an increase in pressure.

4. How does temperature affect pressure?

As temperature increases, pressure also increases. This is due to the fact that as temperature increases, the average kinetic energy of the molecules in a gas also increases. This leads to more collisions between molecules and an increase in pressure.

5. What is the difference between absolute pressure and gauge pressure?

Absolute pressure is the total pressure exerted by a gas, including atmospheric pressure. Gauge pressure, on the other hand, is the pressure relative to atmospheric pressure. This means that gauge pressure will read as 0 when the pressure is equal to atmospheric pressure.

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