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

  • Thread starter Noman Rasheed
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In summary: 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= ?
  • #1
Noman Rasheed
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1
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.
H6v1yqJ.png


I need to find ΔS and PF.

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?
 

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  • #2
Noman Rasheed said:
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 PF.

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?
 
  • #3
Chestermiller said:
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?
 
  • #4
Noman Rasheed said:
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?
 
  • #5
Chestermiller said:
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: pVϒ = 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(Vf1-ϒ - Vi1-ϒ)/(1-ϒ). Still I don't know how to find the value of K.
 
  • #6
Noman Rasheed said:
I am so confused right now.
I have the value of ϒ, which is 1.4. I can also use formula: pVϒ = 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(Vf1-ϒ - Vi1-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)?
 
  • #7
Chestermiller said:
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.
 
  • #8
Noman Rasheed said:
Volume is constant.
And the work the gases do on the rigid container comprising their surroundings?
 
  • #9
Chestermiller said:
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.
 
  • #10
Noman Rasheed said:
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= ?
 
Last edited:
  • #11
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?
 

1. What is ΔS and P(final)?

ΔS (Delta S) is the change in entropy of a system, which is a measure of the disorder or randomness of a system. P(final) is the final pressure of a system, which is a measure of the force exerted per unit area. Both of these terms are important in understanding the thermodynamics and behavior of a system.

2. How do you calculate ΔS and P(final)?

ΔS can be calculated using the formula ΔS = Q/T, where Q is the heat absorbed or released by a system and T is the temperature in Kelvin. P(final) can be calculated using the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

3. Why is it important to find ΔS and P(final)?

ΔS and P(final) are important because they provide valuable information about the behavior and stability of a system. ΔS can indicate whether a reaction or process is spontaneous, and P(final) can give insight into the physical properties and changes of a system.

4. What are some factors that can affect the values of ΔS and P(final)?

The values of ΔS and P(final) can be affected by various factors such as temperature, pressure, volume, and the nature of the substances involved. Changes in these factors can lead to changes in the entropy and pressure of a system.

5. How can ΔS and P(final) be applied in practical situations?

ΔS and P(final) have practical applications in various fields such as chemistry, physics, and engineering. They are used to predict and understand the behavior of chemical reactions, physical processes, and thermodynamic systems. They are also important in designing and optimizing industrial processes.

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