Thermodynamics - intial pressure

[amdma2003]

Homework Statement

Two 800 $$cm^{3}$$ containers hold identical amounts of a monatomic gas at 20 deg C. Container A is rigid. Container B has a 100 $$cm^{2}$$ piston with a mass of 10 kg that can slide up and down vertically without friction. Both containers are placed on identical heaters and heated for equal amounts of time.

What are the initial pressures in containers A and B?
The containers are not heated initially.

Homework Equations

To find the pressure of Container B we can use the equation $$P = \frac{F}{A}$$ where $$F = mg = 10 kg \times 9.8 \frac{m}{s^{2}}$$ and $$A = 100 cm^{2}$$

The Attempt at a Solution

As I have found the Container B to be at 9800 Pascals (by converting cm to meters) I do not know how to approach the problem for finding the pressure for Container A.

 

[andrevdh]

The pressure on a surface is caused by the atoms colliding with it, like a ball rebounding from a wall. This imparts an impulse to the surface - it experiences a force due to the collisions. The strength of these collisions are determined by two factors - the mass and (average) speed of the atoms. The speed of the atoms in both containers are the same since they are at the same temperature and both have atoms with similar mass (the speed would have been different if the mass were not the same, even if the temperature were still the same. That is the temperature is a measure of the [average] kinetic energy of the gas, which depends on both the speed and the mass of the atoms). What can one then conclude about the initial pressure of the gas in container A?

 

[Andrew Mason]

Homework Statement

Two 800 $$cm^{3}$$ containers hold identical amounts of a monatomic gas at 20 deg C. Container A is rigid. Container B has a 100 $$cm^{2}$$ piston with a mass of 10 kg that can slide up and down vertically without friction. Both containers are placed on identical heaters and heated for equal amounts of time.

What are the initial pressures in containers A and B?
The containers are not heated initially.

Homework Equations

To find the pressure of Container B we can use the equation $$P = \frac{F}{A}$$ where $$F = mg = 10 kg \times 9.8 \frac{m}{s^{2}}$$ and $$A = 100 cm^{2}$$

The Attempt at a Solution

As I have found the Container B to be at 9800 Pascals (by converting cm to meters) I do not know how to approach the problem for finding the pressure for Container A.

You can determine P in Container B as you have done except that you also have to add in the atmospheric pressure.

Find PV/n = RT for Container B. You know that PV has to be equal for both since n is the same. The difference in pressure between the two is due to the weight of the piston

AM

 

[andrevdh]

Since V and n is the same for both can't one take your reasoning further and say that

P = nRT/V

should be the same for both?

 

[Andrew Mason]

Since V and n is the same for both can't one take your reasoning further and say that

P = nRT/V

should be the same for both?

V is not necessarily the same for both. V is the volume of the gas, not the container. The position of the piston determines the volume occupied by the gas in B.
-------------

Upon further consideration, I think you must be right. The volume of the "container" in B must be the 800 cm^3. Otherwise, there is not enough information. P_B = P_A.

AM

 

[amdma2003]

I don't understand how the weight of the piston affects the pressure. I thought since the piston is free to move up and down, the pressure is just mg/A.

 

[Andrew Mason]

I don't understand how the weight of the piston affects the pressure. I thought since the piston is free to move up and down, the pressure is just mg/A.

Do a freebody diagram of the forces on the piston.

There are two forces downward: the piston weight (= mg) + the atmosphere (= $P_{atm}A_{piston}$)

There is one upward force: $P_{B}A_{piston}$

Since there is no acceleration, they are equal and opposite forces:$$P_{B}A_{piston} = mg + P_{atm}A_{piston}$$

$$P_{B} = \frac{mg + P_{atm}A_{piston}}{A_{piston}} = \frac{mg}{A_{piston}} + P_{atm}$$

AM