Understanding q: Why does dqsurr = -dqsys?

[santimirandarp]

The question is:

why $dq_{surr}=-dq_{sys}$?

q=heat, surr=surroundings, sys=system.

Is there any simple way to understand this?

 

[PeroK]

The question is:

why $dq_{surr}=-dq_{sys}$?

q=heat, surr=surroundings, sys=system.

Is there any simple way to understand this?

Conservation of energy?

 

[santimirandarp]

Conservation of energy?

How do you derive that expression from the conservation of energy?

 

[PeroK]

How do you derive that expression from the conservation of energy?

If the heat (energy) leaves the system it must go to the surroundings; and, vice versa. The change in one must be equal and opposite to the change in the other.

 

[santimirandarp]

If the heat (energy) leaves the system it must go to the surroundings; and, vice versa. The change in one must be equal and opposite to the change in the other.

I'm sorry but I don't understand that answer

 

[PeroK]

I'm sorry but I don't understand that answer

Is your problem conceptual or mathematical?

Do you understand the concept of conservation? It means that the total amount of something stays the same over time.

Mathematically this means that if you add up all the changes in something it must come to zero. In this case:

Change in energy (system) + change in energy (surroundings) = 0

or:

$dq_{sys} + dq_{sur} = 0$

 

[santimirandarp]

Is your problem conceptual or mathematical?

Do you understand the concept of conservation? It means that the total amount of something stays the same over time.

Mathematically this means that if you add up all the changes in something it must come to zero. In this case:

Change in energy (system) + change in energy (surroundings) = 0

or:

$dq_{sys} + dq_{sur} = 0$

I know maths and conservation.
But why do you say heat is conserved?

 

[PeroK]

I know maths and conservation.
But why do you say heat is conserved?

Because that's what you said in the original post. Your equation is equivalent to conservation of heat energy.

Say, for example, you have:

Change in the number of apples in the system = - change in the number of apples in the surroundings

And you asked "is there a simple way to explain this?" Then I'd say "conservation of apples".

 

[santimirandarp]

Because that's what you said in the original post. Your equation is equivalent to conservation of heat energy.

Say, for example, you have:

Apples put in the barrel 1 = - apples put in barrel 2

And you asked "is there a simple way to explain this?" Then I'd say "conservation of apples".

It is not. The equality I showed is exactly what I don't understand ('why ...'). So I'm asking: where does the equality comes from? (and heat is not so simple as apples).

 

[PeroK]

So I'm asking: where does the equality comes from?

It's the first law of thermodynamics.

 

[santimirandarp]

It's the first law of thermodynamics.

It is not. The first law implies that universe internal energy is conserved and also:

$\Delta U_{sys}=(W+Q)_{sys}=-\Delta U_{surr}=-(W+Q)_{surr}$

so $(W+Q)_{sys}=-(W+Q)_{surr}$
I don't see how it follows that dq=-dq_{surr}

 

[DrClaude]

why $dq_{surr}=-dq_{sys}$?

This is only true in the absence of any work.

 

[santimirandarp]

This is only true in the absence of any work.

I've found it quoted as a general truth. Thanks.

 

[PeroK]

I've found it quoted as a general truth. Thanks.

Are you telling us or asking us? That this is a universal truth? And, that the obvious explantion that it's the first law in the absence of work won't do?

 

[santimirandarp]

Are you telling us or asking us? That this is a universal truth? And, that the obvious explantion that it's the first law in the absence of work won't do?

I'll ask the second part on a different question.

 

[sophiecentaur]

I've found it quoted as a general truth. Thanks.

You would have to quote the source. Either it is wrong, it is about a specific situation or you have misunderstood it.
Anything that’s a "general truth" will be stated in many places.