Calculating ΔS and P(final) for a Diatomic Ideal Gas in a Partitioned System

[Noman Rasheed]

So, there is a problem given, where diatomic ideal gas N₂ is involved. Both blocks have same volume: 1m³. The molar mass of gas is: 28 g/mol. Initial temperature is 300K.

I need to find ΔS and P_F.

First, I did find P₁ by using formula: PV = nRT
so, P₁ = 1*8.3145*300/1 = 2494.35 Pa
and P₂ = 2*8.3145*300/1 = 4988.7 Pa

Finally: I have total moles = 3, and total V = 2 m³.
What should I consider next?

 

[Chestermiller]

So, there is a problem given, where diatomic ideal gas N₂ is involved. Both blocks have same volume: 1m³. The molar mass of gas is: 28 g/mol. Initial temperature is 300K.
View attachment 216245

I need to find ΔS and P_F.

First, I did find P₁ by using formula: PV = nRT
so, P₁ = 1*8.3145*300/1 = 2494.35 Pa
and P₂ = 2*8.3145*300/1 = 4988.7 Pa

Finally: I have total moles = 3, and total V = 2 m³.
What should I consider next?

What does the first law of thermodynamics tell you about the change in internal energy of this system? Based on that, what is the final temperature of the system?

 

[Noman Rasheed]

What does the first law of thermodynamics tell you about the change in internal energy of this system? Based on that, what is the final temperature of the system?

The first law of the thermodynamics says that the change in internal energy = heat added to the system - work done by the system.
However, I can't connect the dots with the final temperature based on this definition. Any hints please?

 

[Chestermiller]

The first law of the thermodynamics says that the change in internal energy = heat added to the system - work done by the system.
However, I can't connect the dots with the final temperature based on this definition. Any hints please?

As I said, in this particular problem, what is the total change in internal energy of the system comprised of the two gases? How much heat is added to the system? How much work do the gases do on their rigid container?

 

[Noman Rasheed]

As I said, in this particular problem, what is the total change in internal energy of the system comprised of the two gases? How much heat is added to the system? How much work do the gases do on their rigid container?

I am so confused right now.
I have the value of ϒ, which is 1.4. I can also use formula: pV^ϒ = K, but I don't know which p should I use. As, I come up with values for pressure. Further, work done could be found out by K(V_f^1-ϒ - V_i^1-ϒ)/(1-ϒ). Still I don't know how to find the value of K.

 

[Chestermiller]

I am so confused right now.
I have the value of ϒ, which is 1.4. I can also use formula: pV^ϒ = K, but I don't know which p should I use. As, I come up with values for pressure. Further, work done could be found out by K(V_f^1-ϒ - V_i^1-ϒ)/(1-ϒ). Still I don't know how to find the value of K.

What is the change in volume of the rigid container holding the gases? Based on this, how much work does the system comprised of the two gases do on their surroundings (I.e., on the rigid container)?

 

[Noman Rasheed]

What is the change in volume of the rigid container holding the gases? Based on this, how much work does the system comprised of the two gases do on their surroundings (I.e., on the rigid container)?

Volume is constant.

 

[Chestermiller]

Volume is constant.

And the work the gases do on the rigid container comprising their surroundings?

 

[Noman Rasheed]

And the work the gases do on the rigid container comprising their surroundings?

I can't find out work done, since I don't have the value of K. I can figure out K, but I just don't know whether I use p₂ or p₁ in the formula.

 

[Chestermiller]

I can't find out work done, since I don't have the value of K. I can figure out K, but I just don't know whether I use p₂ or p₁ in the formula.

The gases do zero work on their surroundings (I.e., the rigid container) because, treating the container as a black box, $\Delta V=0$. And the heat entering is also zero, since the container is insulated. So the change in internal energy= ?

 

[Chestermiller]

Is the partition forced to move gradually, or is it free to move on its own (unconstrained)? Is the partition insulated, so that no heat can pass from one side to the other, or is it conductive to heat?