Undergrad Power equation using heat instead of work

[ikihi]

So the formula for power is Power = work / time. There's two types of energy transfers: heat and work. How do you calculate the power of something using heat energy in BTU/hr when BTU isn't work?

 

[Dale]

That is just a question of semantics. The calculation is fine, only the terminology is problematic.

 

[DaveE]

BTU is work (or energy). 1 BTU = 1055.06 joules = 1055.06 Watt-sec.

 

[ikihi]

BTU is work (or energy). 1 BTU = 1055.06 joules = 1055.06 Watt-sec.

That is just a question of semantics. The calculation is fine, only the terminology is problematic.

Work is mechanical energy moved in a direction and heat is the energy of random particles moving around? So you are saying that heat energy may be used in this equation, even though it says work?

 

[Dale]

Sure. Just change the definition of power from work per time to energy transfer per time. It is just semantics

 

[DaveE]

Work is mechanical energy moved in a direction and heat is the energy of random particles moving around? So you are saying that heat energy may be used in this equation, even though it says work?

yes. Energy is a more fundamental concept than a particular scenario. Energy is often converted from one form to another. For example, consider a Carnot engine that converts heat energy into mechanical energy.

If we didn't know how to convert chemical potential energy (like gasoline) into heat energy (like combustion in cylinders), and then into mechanical energy (like spinning tires), you couldn't drive your car to the grocery store.

Work IS energy, energy IS work. Two different names for the same thing. Which, BTW, I always found annoying; just pick one. I choose "energy".

 

[Dale]

Work IS energy, energy IS work.

I wouldn’t go that far. Work is a credit or debit, energy is the account balance.

 

[ikihi]

yes. Energy is a more fundamental concept than a particular scenario. Energy is often converted from one form to another. For example, consider a Carnot engine that converts heat energy into mechanical energy.

If we didn't know how to convert chemical potential energy (like gasoline) into heat energy (like combustion in cylinders), and then into mechanical energy (like spinning tires), you couldn't drive your car to the grocery store.

Work IS energy, energy IS work. Two different names for the same thing. Which, BTW, I always found annoying; just pick one. I choose "energy".

I wouldn’t go that far. Work is a credit or debit, energy is the account balance.

From what I read: The Second Law of Thermodynamics allows work to be transformed fully into heat, but forbids heat to be totally converted into work. This is confusing because they are not totally interchangeable it seems.
"Heat" is a form of energy in transit: it has thermal energy as the "currency".
Work is a form of energy in transit: mechanical energy as the "currency".

I do not understand why they don't say that heat transfer and work are both just called "energy transfer".

 

[DaveE]

I wouldn’t go that far. Work is a credit or debit, energy is the account balance.

OK. That is how it's used. OTOH it's all the same stuff (money, in this case). You are adding process details to the definition of what it is.

I know what $1000 is but I might not know whether it's entering the bank vault, or whether it's already there. In that world "$" is a unit of magnitude, a description of what it is. Then they have additional process names, like credit, debit, balance...

If you are going to use this definition of work, then you'll have to provide more details on the process side. I would prefer to keep processes separated from identity and quantification. But I know most of the physics world doesn't agree with me. In practice, they would say you "do" work and "store" energy. The physics world isn't very consistent with this approach. Things like position, pressure, temperature, or time aren't treated that way. But, as you said "It is just semantics".

 

[DaveE]

"Heat" is a form of energy in transit

Not always. You can store energy in the form of heat. The translation of equations into human language is fraught with additional complexities. Often you need to know the context for complete understanding.

 

[ikihi]

Not always. You can store energy in the form of heat. The translation of equations into human language is fraught with additional complexities. Often you need to know the context for complete understanding.

Wouldn't "heat" imply a temperature difference? And when there is a temperature difference that suggests that thermal energy will start flowing from hot to cool areas? In other words: heat is an energy transfer of thermal energy. I was using "heat" in a similar manner to "work", in that I was referring to the transfer process.

 

[Dale]

Then they have additional process names

Yes. Work is a process in that sense.

The physics world isn't very consistent with this approach. Things like position, pressure, temperature, or time aren't treated that way.

Probably because none of those things are conserved. Many conserved quantities have something similar either denoting a transfer or a rate of transfer (or both). For energy it is work/power. For momentum it is impulse/force. For angular momentum it is torque. For charge it is current.

 

[DaveE]

For energy it is work/power. For momentum it is impulse/force. For angular momentum it is torque. For charge it is current.

Those all have different units. We aren't discussing work/power. We are discussing work/energy.

 

[Dale]

I do not understand why they don't say that heat transfer and work are both just called "energy transfer".

That is just historical. Originally heat and mechanical work were seen as completely different things.

Then Joule discovered that they both increase the energy of an object, and we missed the first opportunity to change heat to thermal work.

Then Maxwell and others showed that fields could transfer energy. It seemed too cumbersome to add another term, so this transfer was lumped in with work. And we missed another opportunity.

Then we began to understand statistical mechanics and quantum mechanics and that heat is simply ordinary work done on degrees of freedom we don’t keep track of. And we missed a third opportunity.

So at this point the terminology seems unlikely to change in the foreseeable future. I would prefer to call it “thermal work”, but alas.

 

[DaveE]

Wouldn't "heat" imply a temperature difference? And when there is a temperature difference that suggests that thermal energy will start flowing from hot to cool areas? In other words: heat is an energy transfer of thermal energy. I was using "heat" in a similar manner to "work", in that referring to the transfer process.

Yes, that makes sense to me. Again, there is a difference between what people say and what makes sense in basic definitions. You are much more likely to hear about heat energy storage than temperature energy storage, for example.

I think there are two things going one. One is to understand the physics. The other is to understand how to talk about physics.

 

[ergospherical]

@DaveE in this case it's not just semantics, it's an important distinction. The energy $E = E(p,V)$ of a system is a state function, but heat $Q$ and work $W$ are not state functions (they are processes). Similarly the one-form $dE$ is exact whilst the one-forms $dW$ and $dQ$ are not.

 

[DaveE]

@DaveE in this case it's not just semantics, it's an important distinction. The energy $E = E(p,V)$ of a system is a state function, but heat $Q$ and work $W$ are not state functions (they are processes). Similarly the one-form $dE$ is exact whilst the one-forms $dW$ and $dQ$ are not.

OK, a perfectly reasonable definition of the result of a process of changing energy (a discrete chunk of energy). Is there an equivalent word for a cumulative change in angular momentum or charge, if not how do physicists get by without them?

I guess I don't have a problem with the semantics of defining work as a process instead of a thing (or really the result of a process). But I think processes usually require a more detailed description, which makes a unique word for the amount unnecessary. I think we could get by with "power" as a better name for the process of changing energy. Or perhaps change the symbol for work from $W$ to $\Delta E$.

As I said, I know y'all don't agree with me. Maybe because that's what's written in the intro textbooks and we can't get rid of it. I think it's unnecessary and inconsistent, but then, I didn't live in a world without "work" in the physics books. Maybe it's crucial and makes things clearer; except for the OP who appeared confused about work and energy.

 

[DaveE]

OTOH, I don't have a problem with "heat" since it conveys energy in a thermodynamic context. It has the added value of not being confused with ropes and pulleys, or EM.

 

[ergospherical]

In thermodynamics, work $dW$ can be done in several ways
- hydrostatic pressure $-pdV$
- surface tension $\gamma dA$
- electric field $\mathbf{E} \cdot d\mathbf{p}$
- electric current $\Delta \phi dq$
etc.

Consider for example the $pV$ work done by hydrostatic pressure $dW = -pdV$. Since $dW$ is not an exact differential, the work $-\displaystyle{\int_a^b} pdV$ done in going from $(p_1, V_1) \rightarrow (p_2, V_2)$ depends on the path between these points in the $pV$ plane.

Meanwhile energy transferred to the system which isn't be accounted for by work done (as @Dale mentioned, it's wrapped up in degrees of freedom we do not study in detail) is called heat $dQ$. Then the first law of thermodynamics states that $dE = dW + dQ$.

The energy $E$ is a state function therefore $\displaystyle{\int_a^b} dE = E(b) - E(a)$ is independent of the path from state $a$ to state $b$.

 

[Dale]

I think we could get by with "power" as a better name for the process of changing energy.

I agree that power is more useful than work, IMO.

Is there an equivalent word for a cumulative change in angular momentum or charge, if not how do physicists get by without them?

I think it is a bit unrealistic to think that we shouldn’t make and use a word unless we also make and use a word for every other analogous process. Words are made historically and organically, there is no overarching rationale

 

[DaveE]

I think it is a bit unrealistic to think that we shouldn’t make and use a word unless we also make and use a word for every other analogous process. Words are made historically and organically, there is no overarching rationale

Touché. You are 100% correct about this. Still it proves that physics doesn't need "work", people just like it.

 

[ergospherical]

Or perhaps change the symbol for work from $W$ to $\Delta E$.

this is a bad idea because the energy $E$ of the system can also change if heat is added to it i.e. $\Delta E = W + Q$

Still it proves that physics doesn't need "work", people just like it.

cmon, this is a bit silly

 

[Dale]

this is a bad idea because the energy $E$ of the system can also change if heat is added to it i.e. $\Delta E = W + Q$

Of course that could be fixed by calling heat “thermal work”. If I could wave a wand that is what I would do, but the history is too strong.

 

[ikihi]

OK, a perfectly reasonable definition of the result of a process of changing energy (a discrete chunk of energy). Is there an equivalent word for a cumulative change in angular momentum or charge, if not how do physicists get by without them?

I guess I don't have a problem with the semantics of defining work as a process instead of a thing (or really the result of a process). But I think processes usually require a more detailed description, which makes a unique word for the amount unnecessary. I think we could get by with "power" as a better name for the process of changing energy. Or perhaps change the symbol for work from $W$ to $\Delta E$.

As I said, I know y'all don't agree with me. Maybe because that's what's written in the intro textbooks and we can't get rid of it. I think it's unnecessary and inconsistent, but then, I didn't live in a world without "work" in the physics books. Maybe it's crucial and makes things clearer; except for the OP who appeared confused about work and energy.

I was confused about how a unit of energy such as BTU or joules can fit into the power equation where work is. I was confused whether thermal energy transfer is work. Some websites have suggested that it is not. These websites list the term "heat" as similar but different to work: which was where my confusion began. But others have stated that thermal energy transfer it is in fact work. So can I conclude that thermal heat transfer from a temperature difference using radiation, conduction, and convection, is in fact work?

 

[Dale]

But others have stated that thermal energy transfer it is in fact work. So can I conclude that thermal heat transfer from a temperature difference using radiation, conduction, and convection, is in fact work?

I personally would like that, but unfortunately that is not how those words are currently defined and used by the scientific community. The official usage is that work is a transfer of energy other than heat.

 

[pkc111]

Your definition of "work is energy" and "energy is work" contradicts many published definitions of the meaning of "work" in physics.
https://en.wikipedia.org/wiki/Work_(physics)
"In physics, work is the energy transferred to or from an object via the application of force along a displacement."