How Do Initial Pressures Compare in Two Heated Monatomic Gas Containers?

[Kites]

Homework Statement

Two 800 cm^3 containers hold identical amounts of a monatomic gas at 20 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 each container?

Homework Equations

PV = nRT
Q = nC*(delta)T
W = - p*(delta)Volume

The Attempt at a Solution

I've no idea. I've worked on this for 3 hours and I feel that I have two unknowns so far. I want to know the pressure in one of the containers, say V_1 for cylinder one.

So...

P = n*R*T/V_1

But how do I find the moles of this gas? And if that's not needed, what can I possibly do to fix this? I must be missing something obvious.

 

[denverdoc]

I believe you're right, that the pressure in the first container cannot be known from the info given. My guess is this is an oversight, and the assumption is that it is 1atm, because the interesting part of the problem has to do with the piston. So if you assume 1atm initially can you compute the pressure of the second vessel when the piston is in its equilibrium position?

 

[m2003]

I would first start by identifying the key variables and relationships in this scenario. We have two containers, A and B, with identical amounts of a monatomic gas at the same temperature and heated for the same amount of time. The only difference between the two containers is that container B has a piston that can slide up and down. This suggests that the volume of container B can change, while the volume of container A remains constant.

We can use the ideal gas law, PV = nRT, to relate the pressure, volume, and temperature of the gas. Since we are given the volume (800 cm^3) and temperature (20 C) of the gas in both containers, we can calculate the initial pressure in each container using this equation. However, we do not have enough information to directly calculate the number of moles (n) of gas in each container. This is where the second equation, Q = nC*(delta)T, comes in. This equation relates the change in heat (Q) to the number of moles (n) of gas and the specific heat capacity (C) of the gas. Since the gas in both containers is heated for the same amount of time, the change in heat will be the same for both containers. This means that the number of moles of gas in each container must also be the same.

To find the initial pressure in each container, we can use a combination of these equations. Since the number of moles is the same in both containers, we can set the two equations equal to each other and solve for the initial pressure in terms of the unknown number of moles. This will give us a ratio of the initial pressures in container A and B, which we can then use to solve for the individual pressures.

In summary, to find the initial pressures in each container, we will need to use the ideal gas law and the equation for change in heat to create a system of equations that we can solve for the unknown variables. This process may seem daunting, but it is a common approach in science and will help us determine the initial pressures in both containers.