Work done by and on a gas

[Snowbeavers]

I am studying gas systems and am confused because I have conflicting equations from different sources.

From a Chem lecture, the teacher says that
Change in E=q + w and w=-p(change in V)


However, in other books, I have read it as U=Q-W

Also, W= p (change in V)


Which is correct???

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[homestar]

Both of those equations are correct. I ran into this problem as well. It seems that physicists prefer one convention and chemists prefer another. The difference between the two equations is how work and heat are defined.

In the equation with the negative sign (U=Q-W), work is defined as work performed by a system; heat is defined as heat gained by the system. In this version of the First Law of Thermodynamics, the sign conventions are being defined for you.

In the alternate version (which I prefer, because there's no confusion--you just have to know what the signs MEAN), the sign conventions are not explicitly defined: U = q + w.

It is important to understand that a loss of heat or work performed by the system on the surroundings represents a loss of energy by the system. Then you know that both of those cases are negative. On the other hand, if the system gains heat, or has work performed on it by the surroundings, then the energy change is positive.

In summary, an energy loss by the system to the surroundings is negative; an energy gain by the system from the surroundings is positive.

So, if you plug and chug the numbers in both of the formulas with this information, you obtain the same result. I don't know which is expected on the MCAT.

Best,
Homestar

 

[Snowbeavers]

Both of those equations are correct. I ran into this problem as well. It seems that physicists prefer one convention and chemists prefer another. The difference between the two equations is how work and heat are defined.

In the equation with the negative sign (U=Q-W), work is defined as work performed by a system; heat is defined as heat gained by the system. In this version of the First Law of Thermodynamics, the sign conventions are being defined for you.

In the alternate version (which I prefer, because there's no confusion--you just have to know what the signs MEAN), the sign conventions are not explicitly defined: U = q + w.

It is important to understand that a loss of heat or work performed by the system on the surroundings represents a loss of energy by the system. Then you know that both of those cases are negative. On the other hand, if the system gains heat, or has work performed on it by the surroundings, then the energy change is positive.

In summary, an energy loss by the system to the surroundings is negative; an energy gain by the system from the surroundings is positive.

So, if you plug and chug the numbers in both of the formulas with this information, you obtain the same result. I don't know which is expected on the MCAT.

Best,
Homestar

Thanks that helps a lot. So I read that work is actually a scalar quantity but in a sense, doesn't the sign denote a vector quantity?

 

[homestar]

Thanks that helps a lot. So I read that work is actually a scalar quantity but in a sense, doesn't the sign denote a vector quantity?

I don't know--I'm not a physicist. It is a scalar though. A scalar has magnitude and a vector has magnitude and direction.

As I said before, the negative denotes whether energy is flowing out of, or into a system.

That's my best response.