Change in Internal Energy Equation

[tuhtles]

I'm a little bit confused by what the equation for the first law of thermodynamics really is.

From TBR, the energy internal is ΔE = Q - PΔV

However, on kaplan's mcat formula sheet it says ΔE = Q - W
Work (W) = -PΔV, which would make kaplan's formula into ΔE= Q - (-PΔV) = Q + PΔV

So now I'm kinda confused... which one is it? 😕

Referring back to the formula sheet from my physics course it has ΔE = Q + W
where W = -PΔV, which would make ΔE = Q - PΔV. This agrees with TBR and goes against kaplan.

Google gave me mixed results. I think I'm missing something here.

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[Romz]

I'm a little bit confused by what the equation for the first law of thermodynamics really is.

From TBR, the energy internal is ΔE = Q - PΔV

However, on kaplan's mcat formula sheet it says ΔE = Q - W
Work (W) = -PΔV, which would make kaplan's formula into ΔE= Q - (-PΔV) = Q + PΔV

So now I'm kinda confused... which one is it? 😕

Referring back to the formula sheet from my physics course it has ΔE = Q + W
where W = -PΔV, which would make ΔE = Q - PΔV. This agrees with TBR and goes against kaplan.

Google gave me mixed results. I think I'm missing something here.

All depends on how you define work done. IS work done on a system positive or negative? That should be the key difference between Kaplan and TBR; the way they denote work done by a system.

I have no other explanation.

 

[frochocinco]

Agreeing with Domenic, it depends whether the work is positive or negative, however, the thing that you should be able to recognize is that if PV work is done on a system, regardless of whether the volume is increasing or decreasing, it indicates that the change in energy is NOT entirely due to a change in heat, but also to PV work.

This all relates back to the first law of thermodynamics that states that any change in energy in a system is due to either heat or work. depending on what is happening to the system and whether it is gaining or loosing energy determines whether PV is positive or negative

 

[tuhtles]

Ah, this makes more sense. That's what I was thinking but remembering back I always had an issue getting the convention of the +/- for work so the overall equation was kinda cloudy for me.

Just to see if I've got this...

So let's say we have that generic piston situation where gas is inside the container.
Let's say the system is the gas and the surrounding is the external environment

So if the the piston expands, the volume increases and the gas (system) is doing work on the environment (surrounding). So this would mean W = (-) for the gas because it is losing energy since it's using it for work and W = (+) for the environment because it's having work done on.

So since W = (-) for the gas, this means that relative to the environment the internal energy of gas has decreased where as the internal energy of the environment has increased bceause W = (+) for the environment.

Did I get this right?

Also, when an object is in free fall, is the work done by gravity (-) because gravity is "doing work"" on the object and therefore losing "energy"?
But then...
Work = Force x distance
And object falling would be moving in the same direction as the gravitational force, so based on that equation, W = (+) for free fall objects.

I'm not sure which approach makes is right here.

I remember a TBR question asking if the work was -/+ for gravitational force on a free fall object and moving an object upward. Don't remember the answer/concepts of work convention

Thanks for helping out btw!

 

[Romz]

Ah, this makes more sense. That's what I was thinking but remembering back I always had an issue getting the convention of the +/- for work so the overall equation was kinda cloudy for me.

Just to see if I've got this...

So let's say we have that generic piston situation where gas is inside the container.
Let's say the system is the gas and the surrounding is the external environment

So if the the piston expands, the volume increases and the gas (system) is doing work on the environment (surrounding). So this would mean W = (-) for the gas because it is losing energy since it's using it for work and W = (+) for the environment because it's having work done on.

So since W = (-) for the gas, this means that relative to the environment the internal energy of gas has decreased where as the internal energy of the environment has increased bceause W = (+) for the environment. That being said, I always do get a little confused when dealing with work and gravity tho.

Did I get this right?

Also, when an object is in free fall, is the work done by gravity (-) because gravity is "doing work"" on the object and therefore losing "energy"?
But then...
Work = Force x distance
And object falling would be moving in the same direction as the gravitational force, so based on that equation, W = (+) for free fall objects.

I'm not sure which approach makes is right here.

I remember a TBR question asking if the work was -/+ for gravitational force on a free fall object and moving an object upward. Don't remember the answer/concepts of work convention

Thanks for helping out btw!

Hey, if you choose to denote it like that, then it's right!

When i read the problem, I saw that work was being done BY the gas ONTO the system.

Work done BY a gas using Kaplan's formula is (+). The system is doing NEGATIVE work (having work done on it) so work done BY the system is (-) (work done ONTO the system is (+). Delta U = Q - W with my reasoning. You can see the internal E of my system is decreasing through my formula. I read your explanation and saw that you concluded that internal E decreases, which is correct. 👍

Gravity looses energy?? I never knew gravity could loose energy. Not trying to sound like an ass but I have no clue what that meant?? 😕. I would approach that problem again denoting a direction in which gravity acts and focus on my object.


Edit: Thought it out

W = F x D

F = ma. Assume i'm applying a force to move my object up. Gravity vector is pointing against my object. I.E. My object has a negative acceleration. Therefore, my overall force has a negative sign on it because acceleration is negative as well. WORK DONE BY MY OBJECT IS NEGATIVE (work being done on my object). WORK DONE BY GRAVITY IS THEREFORE POSITIVE WHEN I LIFT MY OBJECT UP AGAINST GRAVITY. This makes sense! My object is having work done on it by gravity, therefore increasing it's internal/potential energy. We can see this via U = Q - W. No heat involved here so Q = 0. U = -W. We said work done by my object is negative, so U = -(-W); My change in internal energy is positive; makes sense as we gain potential E going up according to PE = U = mgh.

I hope that makes sense.