[Hapster]

"A sample of an ideal gas at 15.0 atm and 10.0 L is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature.  Calculate the work in units of kJ for the gas expansion. (Hint: Boyle's law applies)."

I am really stuck with this problem...

Setting up Boyle's law (P1V1=P2V2) is the main step I'm having trouble with...

I know that P1 = 15 atm and V1 = 10 L, but what would P2 be?  Once I get that, I can solve for V2 and plug the difference between V1 and V2 into the work eqution for an expanding gas:

Work = -(Pressure)(Change in Volume)

So the only thing I really need help with is determining V2... Any hints would be appreciated...

By the way, the answer is -13.2 kJ. 

[enahs]

Call me crazy, but did you not just say the pressure was constant?

[Hapster]

Call me crazy, but did you not just say the pressure was constant?

Yes, the external pressure is constant...

[SudsMcDuff]

Well, I'm new here, but I'd be happy to help you out. 

You did say the external pressure was constant and not the internal pressure, but the fact that the external pressure is constant is important!

Personally, I think it's important to look at these types of problems conceptually. If you start out at 15 atm and 10 L, and you know that the gas is expanding, when does it stop expanding? It doesn't expand forever, right?

So if, in fact, you know that the external pressure is a constant 2 atm, then that is the final pressure, both internal and external; reason being is that the overall system must come to equilbrium. The internal pressure of the gas shouldn't exceed the external pressure (unless it is heated) and it also shouldn't go below it -- if it does go lower than 2 atm, it contracts!

Now that you know that P2 = 2 atm, you can use Boyle's law to solve for V2, and from there calculate the work done.

[adwina]

I see there are many views for this old post. The information on it was good but incomplete.

Correct, since the constant external pressure is 2.00atm that is your P2 for Boyle's Law to find V2.

But then you need to place find the work. w= P(ΔV)

In this case our pressure is negative because energy flows out of the gas.
so w= -2.00atm*(65L)=  -130L·atm

But the question wants work in kJ so it first needs converted to J then kJ

-130L·atm (101.3J/L·atm)= -13169J /1000J/kJ= -13.169

So then you get the -13.2kJ as your answer.

I hope this helps future people who open this post.