# Finding the work done by a gas under quasi-static, isothermal expansion

1. So, an ideal gas is initially at 293K and 200kPa, and has a volume of .004m3
It undergoes a quasi-static, isotheral expansion until its pressure is reduced to 100kPa
What is the Work done by the gas

2.I know that for isothermal conditions W=nRTln(Pf/Pi)

3. my first attempt was making n=1 and Pf=200kPa and Pi=100kPa
i got W to be 1685w.

My first problem with this is that I don't actually know what n is, and i'm not even sure what Pi and Pf are, can't find it in my lecture notes anywhere.

My next step was to isntead of guessing n=1, make PV=nRt because I have P and V, but i'm not sure which P to use.

I know this dosen't seem like a difficult problem, but i won't be getting the answers until next month, so any guidance will be appreciated

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gabbagabbahey
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[
My next step was to isntead of guessing n=1, make PV=nRt because I have P and V, but i'm not sure which P to use. [/b]
Both P and V change during the expansion. You don't know the final volume, but you do know the initial volume. So, use the initial pressure as well.

Andrew Mason
Homework Helper
1. So, an ideal gas is initially at 293K and 200kPa, and has a volume of .004m3
It undergoes a quasi-static, isotheral expansion until its pressure is reduced to 100kPa
What is the Work done by the gas

2.I know that for isothermal conditions W=nRTln(Pf/Pi)
It should be Pi/Pf.

dW = PdV. If you substitute P = nRT/V (where T is constant since it is isothermal) you get:

$$\int_{V_i}^{V_f} PdV = nRT\int_{V_i}^{V_f} dV/V = nRT\ln (\frac{V_f}{V_i})$$

Since, by the ideal gas law, PiVi/Ti = PfVf/Tf, Vf/Vi = Pi/Pf (where Ti and Tf are equal)

3. my first attempt was making n=1 and Pf=200kPa and Pi=100kPa
i got W to be 1685w.
My first problem with this is that I don't actually know what n is, and i'm not even sure what Pi and Pf are, can't find it in my lecture notes anywhere.

My next step was to instead of guessing n=1, make PV=nRt because I have P and V, but i'm not sure which P to use.
You have to find n. Use the ideal gas law:

PV=nRT

You know Pi, Vi and Ti so you can find n. n does not change.

AM