Entropy and Adiabatic Expansion

In summary, the problem involves Argon gas expanding adiabatically from 0.01 m3 to 0.029 m3 while doing work on a piston. The task is to calculate the contributions to the entropy change, specifically the change in entropy due to the volume change alone. This is discussed in Moore, T7.4. The answer is 3.549 J/K. The next part of the problem involves finding the final temperature if the expansion is adiabatic. To solve this, the adiabatic equation needs to be used along with the information already given about the number of moles and molar mass of Argon. The final temperature, Tf, is not given and needs to be calculated.
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Homework Statement


Argon gas, initially at pressure 100 kPa and temperature 300 K, is allowed to expand adiabatically from 0.01 m3 to 0.029 m3 while doing work on a piston.

In this problem you will calculate the contributions to the entropy change, as discussed in Moore, T7.4.

a) What is the change in entropy due to the volume change alone, ignoring any effects of changing internal energy?
DS = 3.549 J/K *
OK

b) If the expansion is adiabatic, what is the final temperature?

Tf = K

-------

Part A was fairly easy. We're doing homework in arears. We are already on to special relativity so I'm trying to remember entropy (and a lot of this seems to be going back even further to PV diagrams which was 2 units ago). I'm struggling to remember how to do this. There are more questions to this problem, but they all stem around part B.

Homework Equations


PV = nRT -> I calculated that there are .4009 moles.
From my number of moles and the molar mass of argon I know that my sample weighs 16.02 g.

The Attempt at a Solution



I had a couple of equations but I keep needing P1 AND T1. I need another equation. Can someone please provide some guidance?
 
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I think I need to use the adiabatic equation, but I'm not sure how to set it up or what other information I need to solve for Tf. Any help is greatly appreciated!
 

Related to Entropy and Adiabatic Expansion

1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. It is a thermodynamic quantity that describes the distribution of energy and matter within a system.

2. How does entropy relate to adiabatic expansion?

Adiabatic expansion is a process in which a system expands without exchanging heat with its surroundings. During this process, the entropy of the system remains constant. This means that the disorder or randomness of the system does not change.

3. What is the equation for calculating entropy change during adiabatic expansion?

The equation for calculating entropy change during adiabatic expansion is ΔS = nCvln(Tf/Ti), where ΔS is the change in entropy, n is the number of moles of gas, Cv is the molar heat capacity at constant volume, Tf is the final temperature, and Ti is the initial temperature.

4. How does adiabatic expansion affect temperature and pressure?

During adiabatic expansion, the temperature of the system decreases due to the decrease in internal energy. This is because the system is doing work on its surroundings without gaining or losing heat. The pressure also decreases because the volume of the system increases.

5. What is the significance of adiabatic expansion in thermodynamics?

Adiabatic expansion is important in thermodynamics because it allows us to understand and predict the behavior of gases under specific conditions. It also helps us understand the relationship between temperature, pressure, volume, and entropy. Adiabatic expansion is a fundamental process in many engineering applications, such as in the design of engines and turbines.

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