Change in entropy at constant temperature

In summary, the conversation is about calculating the entropy change of a perfect gas at constant temperature when it is compressed from an initial pressure to a final pressure. The relevant equations are the first law and the work for isothermal expansion. By combining these equations and using the ideal gas law, the answer can be calculated.
  • #1
ricof
14
0

Homework Statement



Calculate the entropy change when 0.011m3 of a perfect gas at a constant temperature of 273K is compressed from an initial pressure 1x10^5 N/m/m to a pressure of 1x10^6 N/m/m.

I know the equation but cannot work out Q! Please help!

Homework Equations



dS=Q/T

The Attempt at a Solution

 
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  • #2
Hi ricof, welcome to PF. Can you combine the First Law with what you know about the energy of an ideal gas at constant temperature?
 
  • #3
Some more relevant equations.
The first law
[tex]\Delta E=Q+W[/tex]
Work for isothermal expansion
[tex]W=-nRTln\frac{V_{f}}{V_{i}}[/tex]

If you combine this with what you know about change in internal energy at constant temperature, like Mapes said, and that integral of yours, you can figure out the answer.
 
  • #4
Because T is constant, there is no change in internal energy right?

And also, in the above equation for isothermal expansion, how is n calculated?
 
Last edited:
  • #5
ricof said:
Because T is constant, there is no change in internal energy right?

And also, in the above equation for isothermal expansion, how is n calculated?

Agreed on the first question. For the second: apply the ideal gas law.
 
  • #6
Ok, so as dE = 0,

Q = -W

and as PV = nRT,

-W=PV ln (v1/v2) which is Q

Thanks guys, my answer is correct. Thanks for helping!
 

1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. It is often described as the amount of energy that is unavailable to do work in a system.

2. How does entropy change at constant temperature?

If the temperature of a system remains constant, the change in entropy is determined by the change in disorder of the system. If the disorder increases, the entropy also increases. If the disorder decreases, the entropy decreases.

3. How does the second law of thermodynamics relate to entropy at constant temperature?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. At constant temperature, this means that the disorder in the system will also increase, leading to an increase in entropy.

4. Can entropy be negative at constant temperature?

No, at constant temperature, entropy cannot be negative. This is because the second law of thermodynamics dictates that the total entropy of a closed system will always increase, and entropy cannot be negative.

5. How does the change in entropy at constant temperature affect the spontaneity of a reaction?

The change in entropy at constant temperature can determine the spontaneity of a reaction. If the change in entropy is positive, the reaction is more likely to be spontaneous. If the change in entropy is negative, the reaction is less likely to be spontaneous.

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