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Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: Strike on January 26, 2012, 01:35:38 AM

Title: Finding work in isothermal process
Post by: Strike on January 26, 2012, 01:35:38 AM

Hello, this seems like a very easy/simple question but I'm stuck..

Calculate the work w when 8.7 litre of an ideal gas at an initial pressure of 3.4 atm is expanded or compressed isothermally to a final volume of 3.4 litres reversibly. Give your answers in J. (Ans: 2816.0J)

The formula I'm trying to use is w = -nRT ln(V2/V1) - used for reversible, isothermal and ideal gas processes. (Closest I could come up with)

But the question does not provide how many moles or an initial/final temperature.

Title: Re: Finding work in isothermal process
Post by: UG on January 26, 2012, 01:42:21 AM

A fairly reasonable assumption may be that the temperature is 298.15 K, its an isothermal process so there is no temperature change. Then using the ideal gas law, calculate the number of moles of gas present, this will remain constant for either volume. You can then substitute these two variables into the equation w = -nRT ln(V2/V1), the answer should be similar to 2816 J.

Title: Re: Finding work in isothermal process
Post by: Strike on January 26, 2012, 01:48:51 AM

Is there anyway of calculating work without making any assumptions? (Maybe assuming the temperature of 25C was just a coincidence in this question).

Title: Re: Finding work in isothermal process
Post by: UG on January 26, 2012, 02:01:36 AM

It doesn't matter what temperature you assumed the process was taking place, you could have used 1000 K and still got the same answer. Since n and T are proportional, changing one variable will also change the other so when you come to substituting into the formula, everything cancels out and the final answer stays the same :)

Title: Re: Finding work in isothermal process
Post by: Strike on January 26, 2012, 02:09:54 AM

Ohhhh... Thank you very much!

Title: Re: Finding work in isothermal process
Post by: juanrga on January 26, 2012, 06:41:36 AM

Quote from: Strike on January 26, 2012, 01:35:38 AM

Hello, this seems like a very easy/simple question but I'm stuck..

Calculate the work w when 8.7 litre of an ideal gas at an initial pressure of 3.4 atm is expanded or compressed isothermally to a final volume of 3.4 litres reversibly. Give your answers in J. (Ans: 2816.0J)

The formula I'm trying to use is w = -nRT ln(V2/V1) - used for reversible, isothermal and ideal gas processes. (Closest I could come up with)

But the question does not provide how many moles or an initial/final temperature.

Since PV = nRT

w = -PV ln(V2/V1)

without any assumption about T.