# Volume of gas in a cylindrical vessel on which a piston has been placed

• merbear
In summary: P1=.6*9.8*(K-353) V= 3.15 m^3 In summary, when a cylinder with a movable piston is heated from 20 degrees Celsius to 80 degrees Celsius, a mass of 0.3 kg must be placed on top of the piston to maintain the position. The volume of the gas is 53.9 m^2.
merbear
[SOLVED] volume of gas in a cylindrical vessel on which a piston has been placed

## Homework Statement

A cylindrical vessel with a tight but movable piston is placed in a vertical position so that the piston, whose area is 60 cm2, is subject to atmospheric pressure. When the gas in the vessel is heated from 20oC to 80oC, a 0.6 kg mass must be placed on top of the piston to hold it at the position it occupied at lower temperature.
What is the volume of 0.3 mol of the gas?

Pv=nRT

## The Attempt at a Solution

Since we were given the moles of gas (.3 mol) and we know R since it's a constant, I assumed that the pv=nRT would be the correct equation. I found the pressure of the cylinder with the weight on to be the pressure by the weight: P=F/A= [(.6 kg * 9.8 m/s^2)]\.6m^2. The temperature I put was 353K - that of the second cylinder.

I got a volume of 53.9 m^2 but I know that the volume must be much greater, given the size of the cylinder in the problem. I don't know how else to go about the problem so I would appreciate any help.

Thank-you!

> What is the volume of 0.3 mol of the gas?

Under what T and P? Without that, the question is meaningless. Also, it is not mentioned in the problem that the amount of gas is 0.3 moles. The length of the cylinder is also not given.

What are known are these:

P1/T1 = P2/T2, since the volume remains the same.
P2 - p1 = W/A, where W is the weight of the mass, A = area of piston.

So, P1 and P2 both may be found.

Still a bit confused about the cylinder question

I don't understand what you mean when you say, 'under what temperature and pressure'. The question stated that you had one cylinder at 20 degrees and the other one with the weight on it at 80 degrees. It also stated that the piston is subjected to atmospheric pressure. Does the atmospheric pressure not need to be accounted for?

I see how you were saying to solve p1 and p2, but I don't see where to go from there. Would you use the pressure difference to solve for the volume of gas using pv=nRT?

merbear said:
I don't understand what you mean when you say, 'under what temperature and pressure'. The question stated that you had one cylinder at 20 degrees and the other one with the weight on it at 80 degrees. It also stated that the piston is subjected to atmospheric pressure. Does the atmospheric pressure not need to be accounted for?

I see how you were saying to solve p1 and p2, but I don't see where to go from there. Would you use the pressure difference to solve for the volume of gas using pv=nRT?

The question should have been formulated more precisely. In the main problem, it is not mentioned that there were 3 moles of gas. At the very last, it is asked, "What is the volume of 0.3 mol of the gas?", which does not imply that there were 3 moles inside. Anyway, let it go.

The P_atm is acting on both cases and is included in P1 and P2. In fact, if the piston is very light, P1 = P_atm. But we can do without knowing the value of P_atm.

P1V = nRT1 and P2V = nRT2 =>
(P2-P1)V= nR(T2-T1).

You can get V now.

## 1. How is the volume of gas affected when a piston is placed on top of a cylindrical vessel?

When a piston is placed on top of a cylindrical vessel, the volume of gas inside the vessel decreases. This is because the piston compresses the gas, causing it to occupy a smaller space.

## 2. What factors affect the volume of gas in a cylindrical vessel with a piston?

The volume of gas in a cylindrical vessel with a piston is affected by several factors, including the temperature, pressure, and amount of gas present. Changes in these factors can cause the volume of the gas to increase or decrease.

## 3. How can the volume of gas in a cylindrical vessel be calculated?

The volume of gas in a cylindrical vessel can be calculated using the ideal gas law, which states that the volume is directly proportional to the temperature and amount of gas present, and inversely proportional to the pressure. This can be expressed as V = nRT/P, where V is the volume, n is the number of moles of gas, R is the ideal gas constant, T is the temperature, and P is the pressure.

## 4. What happens to the volume of gas in a cylindrical vessel as the piston is moved?

As the piston is moved, the volume of gas in the cylindrical vessel changes. If the piston is moved downwards, the volume of gas decreases as the gas is compressed. If the piston is moved upwards, the volume of gas increases as the gas expands.

## 5. How does the volume of gas in a cylindrical vessel change with temperature?

The volume of gas in a cylindrical vessel is directly proportional to the temperature, according to the ideal gas law. This means that as the temperature increases, the volume of gas also increases, and vice versa. This relationship is known as Charles' Law.

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