# Change in entropy at constant temperature

1. ### ricof

14
1. The problem statement, all variables and given/known data

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!

2. Relevant equations

dS=Q/T

3. The attempt at a solution

2. ### Mapes

2,532
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. ### cavalier

29
Some more relevant equations.
The first law
$$\Delta E=Q+W$$
Work for isothermal expansion
$$W=-nRTln\frac{V_{f}}{V_{i}}$$

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. ### ricof

14
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: Nov 21, 2009
5. ### Mapes

2,532
Agreed on the first question. For the second: apply the ideal gas law.

6. ### ricof

14
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!

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