Help with Pressure Problem: Estimating Maximum Force

[clipperdude21]

Pressure Problem Please Help!

1. One mole of gas at 300 K is enclosed within a 6L container covered by a sliding piston exposed to the atmosphere. The area of the piston is 50 cm^2. An external force Fext is exerted on the piston
(a) We want to use the gas container and piston as a shock absorber for some machine. Estimate the maximum force that this shock absorber can handle. Hint( Think about what would happen if we continue to compress the gas. Estimate the molar concentration at which gas can no longer be considered as dilute.

Homework Equations

3. I am not sure how to do this. Can i get some help on how to get started? I just figured out something. I used the concentration of water at room temperature which is 55.5 M and converted it to get 55500 mol/m^3. I then plugged it into PV=nRT and solved for P, where P=cRT. I got a pressure of like 124 million pascals. I then used P=F/A and solved for force using the area given and got around 620,000 N. Does this look right?

 

[anathema]

Hello there,

Thank you for reaching out for help with your pressure problem. I can help guide you through the steps to solve this problem.

First, let's review the given information. We have a 6L container with 1 mole of gas at 300 K (room temperature). The piston has an area of 50 cm^2 and an external force, Fext, is being exerted on it.

To answer the first question, we need to think about what would happen if we continue to compress the gas. As the gas is compressed, the pressure inside the container will increase. This pressure will eventually reach a point where it is equal to the external force, Fext, being exerted on the piston. At this point, the gas will no longer be able to compress and the piston will stop moving. This is known as the maximum force that the shock absorber can handle.

To estimate this maximum force, we need to calculate the pressure at which the gas can no longer be considered dilute. This means that the gas is no longer following the ideal gas law, PV=nRT. Instead, we need to use the Van der Waals equation, which takes into account the volume of the gas molecules and the attractive forces between them. The Van der Waals equation is given by:

(P + a(n/V)^2)(V - nb) = nRT

Where:
P = pressure
n = moles of gas
V = volume
T = temperature
a and b are constants specific to the gas

We can rearrange this equation to solve for pressure:

P = (nRT)/(V - nb) - a(n/V)^2

To estimate the molar concentration at which the gas can no longer be considered dilute, we can use the expression for molar concentration, c = n/V.

Now, let's plug in the given values into the Van der Waals equation and solve for the pressure at which the gas can no longer be considered dilute.

P = (1 mol)(0.08206 L·atm/mol·K)(300 K)/[(6 L) - (1 mol)(0.04267 L/mol)] - (0.4275 L^2·atm/mol^2)(1 mol)/(6 L) = 45.85 atm

Therefore, the maximum pressure that the shock absorber can handle is 45.85 atm.

 

[ogb p]

Your approach looks correct. To estimate the maximum force that the gas container and piston can handle, we can use the ideal gas law, PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We know the volume and temperature in this scenario, so we can solve for pressure.

Next, we can use the formula P=F/A, where P is the pressure, F is the force, and A is the area of the piston. This will give us an estimate of the maximum force that the gas container and piston can handle.

However, it is important to keep in mind that this is just an estimate and the actual maximum force may vary depending on factors such as the type of gas and the strength of the container and piston. It is always best to consult with an engineer or conduct further experiments to determine the exact maximum force that the shock absorber can handle.