# Question on Thermodynamics Problem

• D_Tr
In summary, the final pressure inside the container is 421 kPa and the air composition is 79% nitrogen and 21% oxygen.
D_Tr
Hello PF people! This is my first topic on the forum. I basically have a question on a problem that was on a thermodynamics exam. I have the solution that was posted by the professor after the exam but I have a question on it. I asked the professor but I wasn't completely satisfied. So:

## Homework Statement

Within a container of constant volume V0, there are initially 100 moles of N2 at pressure P1 = 400 kPa. Using a heat exchanger, the temperature inside tha container is held constant at equal to the environment's temperature, T0 = 300 K. The container's wall is made of a ceramic that allows O2 to pass through, but not N2. N2 and O2 are considered ideal gases and the air in the environment contains 79% N2 and 21% O2. We expose the container to the environment and wait for equilibrium to be reached. Calculate:
a) The final pressure and air composition inside the container.
b) The change in the entropy of the universe during the transition to the final state.

## Homework Equations

We basically need the state equation of the ideal gases, PV = nRT
We also need the equations for entropy change during mixing/unmixing transfering heat and compressing ideal gases.

## The Attempt at a Solution

The first one (a) is easy. The chamical potential of O2 will be equal inside and outside of the container, which means, since the gases are ideal, that the partial pressure of O2 will be equal inside and outside. So we have (Dalton's law for partial pressures):

P1*xO2,inside = PO2,outside => 400*nO2,inside/(100+nO2,inside) = 21kPa => nO2,inside = 5.54 moles and the final pressure inside the container will be 421 kPa.

My question is in (b): If we consider our system to be the gas inside the container and the 5.54 moles of oxygen that enter the container during the transition, is any wirk done on the system?? I would say no but the professor disagrees! Sure, the nitrogen inside the container and the moles that enter the container are compressed, but this is not done via a piston that would give energy to the molecules. The molecules merely pass through the ceramic wall... The professor, in his solution, after calculating the entripy change of the system (unmixing the oxygen from the environment, mixing it with the nitrogen inside the container and then compressing it), calculates the work for isothermal compression of the nitrogen and oxygen to the final pressure. Then this work returns to the environment as heat (since the compression is isothermal), increasing its entropy. But I cannot see how is work done on the system. Any insights? The professor told me that the work is done by the wall but i didn't get it...

P.S.Sorry for the lengthy post but I wanted to be clear.

Last edited:
No work is done in the actual process. But to calculate the entropy change, it is convenient to replace the original (irreversible) process with a substitute sequence of reversible processes that starts at the same state and ends at the same state. In this conceptual process, work is done, possibly by a moving wall or a piston (it doesn't matter, as long as the process is reversible). I can see why your professor's answer was confusing; I would have emphasized that the work is done by a fictional piston in a fictional process. Does this help clarify things?

## 1. What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total energy in a closed system remains constant.

## 2. How is the second law of thermodynamics related to entropy?

The second law of thermodynamics states that in any natural process, the total entropy of a closed system always increases. Entropy is a measure of the disorder or randomness in a system, so this law can also be interpreted as saying that disorder tends to increase over time.

## 3. What is an example of a thermodynamic equilibrium?

A thermodynamic equilibrium is a state in which all the physical properties of a system, such as temperature, pressure, and composition, remain constant over time. An example of this is a cup of hot coffee left on a table to cool down. Eventually, the coffee and the air around it will reach the same temperature, and the system will be in thermodynamic equilibrium.

## 4. How is thermodynamics used in everyday life?

Thermodynamics has many practical applications in our daily lives, such as in heating and cooling systems, engines, and refrigerators. It is also used in the production of electricity and in chemical reactions.

## 5. What is the difference between heat and temperature in thermodynamics?

Heat is a form of energy that is transferred from one object to another due to a difference in temperature. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a substance. In thermodynamics, heat and temperature are related, but they are not the same thing.

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