Internal energy - heat and work

[SephirothXR]

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The equation is U = q+w right? w = -P∆V. I was doing a Kaplan test and it said that U was actually equal to U = q-w. I understand work is negative if the volume change is positive, but I'm confused. Which one is right? And if work is positive, is that work being done by the gas or on the gas?

 

[km1865]

I think its arbitrary what sign you give W as long as you are consistent with it (like, I know it differs in different areas of science like in physics or chem).

But the conventions I personally find easier to understand is that if work is being done BY the gas (i.e. the gas is expanding), then the sign is negative since the gas is losing internal energy by expanding (think of a piston, if a gas is expanding, its DOING work, and expending energy to push the piston, therefore losing internal energy).
Similarly, if a gas is being compressed work is being done ON it by the surroundings, so its internal energy is increasing then the sign is positive.

I was a little confused myself about the convnetion for the first law.. I think thats just a matter of convention as well? Id be cool if someone can clarify that...

 

[SephirothXR]

That makes more sense. No question is going to get that nitty gritty with if it's q+w or q-w, but rather the conceptual understanding of when it loses energy and what work means. Thanks

 

[MShopes]

That makes more sense. No question is going to get that nitty gritty with if it's q+w or q-w, but rather the conceptual understanding of when it loses energy and what work means. Thanks

I don't think it is a personal choice to choose whether to choose - or + and stay consistent with it as this would change the numbers. This rule applies according to EK. If the passage said that the work done by the system is positive, then the work done on the system would be negative and hence the negative sign. But for the major cases, the passage would state that the work done on the system would be positive and hence the positive sign. See what the passage says.

 

[MD Odyssey]

The sign convention is not a matter of personal choice, but different people often write the equation differently.

The change in internal energy for a closed system can be written as dU = dQ + dW, where dQ is the heat transferred INTO the system and dW is the work done ON the system. Both of those are positive quantities.

Now, some people (engineers are really bad about this) tend to write it as dU = dQ - dW, where dQ is still the heat transferred INTO the system, but dW is now the work done BY the system. If a system does work on its surroundings, then the work done by the system is negative, and the equation for the change in internal energy reduces to what we had earlier.

You just have to make sure that equation is written with the proper sign convention and that you don't get lost or confused by what is actually happening. Pick one and just make you write the problem down accordingly.