Entropy = Heat = confusion

[jedidia]

There is something about the relationship between entropy and heat that I just don't get.

When reading about the stuff, it seems to me that there is not only an intricate relationship between the two, but that the two are actually the same. This confuses me, because overall entropy in the universe should be increasing, while it's temperature seems to be decreasing (at least I read that somewhere, and it seems to make sense... otherwise we'd have a perpetual universe...).

So the end point in the universe should be a wide scatter of matter particles close to or at absolute zero. But, if entropy is heat, then that would mean close to zero entropy, which would be less than now (allthough I would consider that state to be less ordered than it is now). So, clearly I got something wrong. Anyone kind enough to explain?

 

[Artlav]

When reading about the stuff, it seems to me that there is not only an intricate relationship between the two, but that the two are actually the same. This confuses me, because overall entropy in the universe should be increasing, while it's temperature seems to be decreasing (at least I read that somewhere, and it seems to make sense... otherwise we'd have a perpetual universe...).

You're not the only one.
I can add to that, that if entropy of the universe increases, it means that the information is being made out of nowhere, causing either some weird external context, or errors in understanding.

But, if entropy is heat, then that would mean close to zero entropy, which would be less than now (allthough I would consider that state to be less ordered than it is now). So, clearly I got something wrong. Anyone kind enough to explain?

As i understood it, it's heat/volume. The universe is assumed to expand, so the temperature will drops, while the amount of heat stays the same.

 

[RisingFury]

Yea... entropy is a difficult thing to understand. Think of it as... cosmic disarray. The higher the entropy, the more disarray there is. The only way to lower entropy is to actually put in work. But if you just let processes do they do best, there will only be more disarray.

Imagine a big, deserted city. Because nobody is putting work in to rebuild the damage, over time, wind, water and earthquakes will destroy it and it won't rebuild itself.


The change of entropy is defined as

Delta-S >= Integral[dQ/T]

If a process is irreversible process (such as dissolving sugar in water - sugar won't just crystallize back by itself, right?), the change of entropy is always

Delta-S > Integral[dQ/T]

But in a reversible process (such as having a piston squeeze gas in a cylinder - the gas increases in pressure and can push the piston back), change of entropy is defined as

Delta-S = Integral[dQ/T] (Of course, that's assuming that your cylinder was thermally insulated and no heat was lost - or that the whole process was just so quick that no heat transferred.)



So... how does this apply to cooling gas?

First let's do a simpler example:
If you have a block of ice that's melting at 0°C (or just slightly above it), the heat required for that is

Q = q * m
q is the specific melting heat - how much heat is required to melt a certain mass

Because the temperature is constant at all times, you don't need to integrate anything and the equation is

Delta-S = Q/T = m*q/T <== That's the change of entropy.

When we then proceed to heat up this molten water from 0°C (or T1) to 10°C (or T2):

The heat required for that is
Q = m * c * Delta-T
c is the specific heat - how much energy is required to heat up a certain mass by 1 K.

But because the temperature is not constant, you need to integrate:

Delta-S = Integral[m*c*dT/T, {T, T1, T2}] - integrating from T1 to T2
Delta-S = m*c*Integral[(1/T)*dT, {T1, T2}] - m and c are constants
Delta-S = m*c*Ln[T]{T1, T2} - integrating 1/T gives you natural log of T
Delta-S = m*c*(Ln[T2]-Ln[T1]) - accounting for temperature ranges
Delta-S = m*c*Ln[T2/T1]


Here's the catch!

Heating the water is a reversible process... which means that cooling it will lower entropy - but that's only if you look at the water/ice itself.

This translates to the "cooling" universe in a way that... even though the gas you're looking at is cooling down, the energy has to go *somewhere*. That means that when you account for the energy that got released by cooling, the entropy of the entire system won't change.

The reason the entropy of the universe is increasing (or staying the same) is that there are several irreversible processes that happen out that.

Take a look at nuclear fusion in stars - hydrogen turns to heavier elements and energy gets released. That means entropy has increased. But although this is a reversible process, heavier elements don't just fall apart by themselves. You need to give them a lot of energy for them to fall apart - but that doesn't happen often. And that means that as heavier elements are created, entropy steadily increases.

 

[Artlav]

cosmic disarray
...
Imagine a big, deserted city. Because nobody is putting work in to rebuild the damage, over time, wind, water and earthquakes will destroy it and it won't rebuild itself.

And, here lays the problem - a city is one point of view, a forest that will grow on it's place in a thousand years is another. It's a change of state.

In other words - something apparently random might make no sense from one angle, and make all the sense from the other. An encoded radio signal might look like a white noise, but it's meaningful in the decoder. An unencoded signal sounds meaningful, but will be white noise in the same decoder.

Information have to be defined relative to something, not as an absolute value. So, the information from a city falling apart or sugar dissolving won't vanish into non-being, but undergo some transformations.

The curious thing is, that the complexity of pretty much everything seems to be increasing, while the notion of entropy seems to suggest that everything is falling apart.

 

[RisingFury]

Information have to be defined relative to something, not as an absolute value. So, the information from a city falling apart or sugar dissolving won't vanish into non-being, but undergo some transformations.

That's why we speak about change in entropy not the value of entropy itself.

The curious thing is, that the complexity of pretty much everything seems to be increasing, while the notion of entropy seems to suggest that everything is falling apart.

Let's not think of think of increasing entropy as "making things fall apart". Think of it as going from a simpler to a more complex system.

If you take a look at the city example, the simple state is when the building material that makes the buildings is in a nice, organized state and the complex state is when the building collapses and spills material all over the place.

With sugar-water example, the simple state is when sugar is organized in crystals and complex state is when it desolves.

In nuclear fusion, simple state is Hydrogen, a more complex state is Helium and even more complex are Carbon and Oxygen and so on...

So entropy doesn't make things fall apart. If that was true, every nucleus higher then Hydrogen would be radioactive.

 

[the.punk]

As RisingFury said you can change/lower the entropy of an inertial system. You must put work/energy in to the system. But this energy doesn't go missing. This the Conservation of energy.
So you can lower the entropy of own inertial system, but the entropy of the universe is increasing.
This is an interesting part of physics. I'm very interested in such things.

RisingFury: Are you studying physics?

 

[Urwumpe]

AFAIR, the expansion of the universe is a process that is keeping entropy in the whole universe constant, but you can have local islands of higher entropy, which suggests that there have to be islands of lower entropy as well.

Maybe, in a highly speculative way, the expansion of the universe is even caused by entropy, the era of the fastest expansion is also the era of most irreversible processes...

 

[Countdown84]

From a qualitative standpoint, I was taught to think of entropy as a measure of the "spread-outedness" of energy.

For example, a cup of boiling hot water contains a lot of thermal energy, concentrated into the water molecules it contains. As the water cools, the thermal energy doesn't go away (conservation of energy), but is spread out among the molecules in the surrounding air, the table, the cup, etc. So the entropy of the system INCREASES because the energy has been distributed among more molecules.

This provides a way to think about the conundrum in post #1. Heat is not equal to entropy, rather heat is a kind of energy, and entropy measures how concentrated (or not) that energy is. As the entropy of the universe increases, all its energy becomes more uniformly spread out among all the matter in existence, and therefore the temperature slowly drops.

 

[the.punk]

AFAIR, the expansion of the universe is a process that is keeping entropy in the whole universe constant, but you can have local islands of higher entropy, which suggests that there have to be islands of lower entropy as well.

Yes. When you look again at the city. The entropy of the city is decreasing, but the entropy of the whole unsiverse is increasing.

Ah and the opposite of entropy is enthalpy.

 

[Artlav]

That's why we speak about change in entropy not the value of entropy itself.

Change is as relative as absolute value. Saying "entropy of the universe increases" implies absolute value.

As RisingFury said you can change/lower the entropy of an inertial system. You must put work/energy in to the system. But this energy doesn't go missing. This the Conservation of energy.
So you can lower the entropy of own inertial system, but the entropy of the universe is increasing.

Does this only sound like a contradiction to me?
Entropy of the universe increase=information increase=energy increase.

 

[the.punk]

From a qualitative standpoint, I was taught to think of entropy as a measure of the "spread-outedness" of energy.

For example, a cup of boiling hot water contains a lot of thermal energy, concentrated into the water molecules it contains. As the water cools, the thermal energy doesn't go away (conservation of energy), but is spread out among the molecules in the surrounding air, the table, the cup, etc. So the entropy of the system INCREASES because the energy has been distributed among more molecules.

This provides a way to think about the conundrum in post #1. Heat is not equal to entropy, rather heat is a kind of energy, and entropy measures how concentrated (or not) that energy is. As the entropy of the universe increases, all its energy becomes more uniformly spread out among all the matter in existence, and therefore the temperature slowly drops.

The enropy increases and the heat decreases.
Enthalpy is the opposite of entropy.

 

[RisingFury]

RisingFury: Are you studying physics?

Yea, I study Astrophysics...

AFAIR, the expansion of the universe is a process that is keeping entropy in the whole universe constant, but you can have local islands of higher entropy, which suggests that there have to be islands of lower entropy as well.

Indeed! But the net across the entire universe is constant or increasing.

Maybe, in a highly speculative way, the expansion of the universe is even caused by entropy, the era of the fastest expansion is also the era of most irreversible processes...

Well, entropy is "part of" the second law of thermodynamics, which states that heat only goes from hotter area to lower are, gas will only flow from area of high pressure to area of low pressure, and so on.

It's probably not just highly speculative way... it's more of a: "It can go one way, but it can't go the other way. Therefore, it can only do that."

Again, imagine a cylinder closed by a piston, with gas inside. Just because you *can* squeeze the gas, that doesn't mean that such a process will happen by itself. But if the gas is squeezed, it will move the the piston - and that is a process that happens by itself.

 

[the.punk]

Does this only sound like a contradiction to me?
Entropy of the universe increase=information increase=energy increase.

No energy is constant. Conservation of energy
Not only heat is energy.
As RisingFury said entropy is more complex increasing.

---------- Post added at 05:56 PM ---------- Previous post was at 05:49 PM ----------

Yea, I study Astrophysics...

Cool to have someone else here how is interested in this.

Indeed! But the net across the entire universe is constant or increasing.

Yes. It must be in level.

Well, entropy is "part of" the second law of thermodynamics, which states that heat only goes from hotter area to lower are, gas will only flow from area of high pressure to area of low pressure, and so on.

It's probably not just highly speculative way... it's more of a: "It can go one way, but it can't go the other way. Therefore, it can only do that."

Again, imagine a cylinder closed by a piston, with gas inside. Just because you *can* squeeze the gas, that doesn't mean that such a process will happen by itself. But if the gas is squeezed, it will move the the piston - and that is a process that happens by itself.

Enthalpy acts against Entropy.
The Entropy is increasing and the heat is decresing. (am I right here?)

 

[Countdown84]

The enropy increases and the heat decreases.
Enthalpy is the opposite of entropy.

Strictly speaking, I'm not sure that's correct. If you consider the whole system (the cup of hot water AND its surroundings), the heat (energy) does not decrease because of conservation of energy. Nevertheless, the entropy does increase.

There is no conservation of entropy, so it's possible for it to decrease without a corresponding change in enthalpy.

Enthalpy is not a concept I'm as comfortable with, but I don't think it's "the opposite" exactly.

 

[the.punk]

Strictly speaking, I'm not sure that's correct. If you consider the whole system (the cup of hot water AND its surroundings), the heat (energy) does not decrease because of conservation of energy. Nevertheless, the entropy does increase.

There is no conservation of entropy, so it's possible for it to decrease without a corresponding change in enthalpy.

Enthalpy is not a concept I'm as comfortable with, but I don't think it's "the opposite" exactly.

I don't mean that that the heat decreases because of consevation of energy. I mean that enthalpy is the decreasing of heat.
The entropy is acting against the enthalpy. The entropy is increasing and the heat is decreasing (enthalpy)

 

[jedidia]

Let's not think of think of increasing entropy as "making things fall apart". Think of it as going from a simpler to a more complex system.

This is a conclusion I have reached on logic reasoning, but it seemed so contrary to what I learned about the concept of entropy: That increasing entropy, as you stated, means increasing disarray. It sounds somewhat strange to think of increasing disarray as increasing complexity. decreasing complexity sounds much more like it, but that's probably where I have my major misconception. Still, how can one talk of increasing disarray within a system when it actually gets more complex?

 

[the.punk]

I don't mean that that the heat decreases because of consevation of energy. I mean that enthalpy is the decreasing of heat.
The entropy is acting against the enthalpy. The entropy is increasing and the heat is decreasing (enthalpy)

Or I correct me. Decreasing of heat is part of the enthalpy.

Enthalpy and entropy are linked together. If entropy increases
the enthalpy decreases. And if enthalpy incrases the entropy decrases.
But in the whole universe the entropy is increasing.

 

[RisingFury]

For example, a cup of boiling hot water contains a lot of thermal energy, concentrated into the water molecules it contains. As the water cools, the thermal energy doesn't go away (conservation of energy), but is spread out among the molecules in the surrounding air, the table, the cup, etc. So the entropy of the system INCREASES because the energy has been distributed among more molecules.

Ok, this provides me with something I can actually calculate...

A pot of water... say 1 kg, boiling at 100°C, in a small, not pressure sealed room of say... 20 m^3 with air temperature of 20°C.

I'm gonna be using m as mass of water, M as mass of air, c as heat capacity of water, cp as heat capacity of air and Ro as air density.

m = 1 kg
T1 = 100°C = 373 K
V = 20 m^3
T2 = 20%C = 273 K
Ro = 1.2 kg / m^3
cp = 1000 J/(kg*K)
c = 4200 J/(kg*K)
-------------------
Delta-S = ?


So first I need to figure out what the temperature of the system will be after the water cools down and air heats up.

Q given off by water = Q received by air
m*c*Delta-T = M*cp*Delta-T
m*c*(T1 -T) = Ro*V*cp*(T-T2)
m*c*T1-m*c*T=Ro*V*cp*T-Ro*V*cp*T2
m*c*T1+Ro*V*cp*T2=Ro*V*cp*T+m*c*T
m*c*T1+Ro*V*cp*T2=T*(Ro*V*cp+m*c)
T = (m*c*T1+Ro*v*cp*T2)/(Ro*V*cp+m*c)
T = 304.9K = 32°C


So... now that I have the end temperature, I can figure out how much the entropy of each part changed.

Here's how the entropy of air changes:

dQ=m*cp*dT

dS=dQ/T
Integrate[dS, {S1, S2}]=Integrate[dQ/T, {T2, T}]
S|{S1, S2} = Integrate[M*c*dT/T, {T2, T}]
S2 - S1 = M*cp*m*Integrate[dT/T, {T2,T}]
Delta-S = M*cp*Ln[T]|{T2, T}
Delta-S = M*cp*Ln[T/T2]
Delta-S = Ro*V*Ln[T/T2]

If we insert numbers...

Delta-S = 963 J/K (this one is positive, so the entropy of air increased).


Since I don't need to account for change from water vapor to water, I can use the same formula to calculate the change of entropy of water.

Delta-S = m*c*Ln[T1/T]
Delta-S = 845 J/K (again, positive)

So the total Delta-S of the system is 1808 J/K.


So yea........ things aren't always as they seem to be.

We've seen that even though water COOLED down, it's entropy still increased. The reason is that the natural state of heat is that it flows from hot to cold... hot -> cold increases entropy.

 

[the.punk]

Ok, this provides me with something I can actually calculate...

A pot of water... say 1 kg, boiling at 100°C, in a small, not pressure sealed room of say... 20 m^3 with air temperature of 20°C.

I'm gonna be using m as mass of water, M as mass of air, c as heat capacity of water, cp as heat capacity of air and Ro as air density.

m = 1 kg
T1 = 100°C = 373 K
V = 20 m^3
T2 = 20%C = 273 K
Ro = 1.2 kg / m^3
cp = 1000 J/(kg*K)
c = 4200 J/(kg*K)
-------------------
Delta-S = ?


So first I need to figure out what the temperature of the system will be after the water cools down and air heats up.

Q given off by water = Q received by air
m*c*Delta-T = M*cp*Delta-T
m*c*(T1 -T) = Ro*V*cp*(T-T2)
m*c*T1-m*c*T=Ro*V*cp*T-Ro*V*cp*T2
m*c*T1+Ro*V*cp*T2=Ro*V*cp*T+m*c*T
m*c*T1+Ro*V*cp*T2=T*(Ro*V*cp+m*c)
T = (m*c*T1+Ro*v*cp*T2)/(Ro*V*cp+m*c)
T = 304.9K = 32°C


So... now that I have the end temperature, I can figure out how much the entropy of each part changed.

Here's how the entropy of air changes:

dQ=m*cp*dT

dS=dQ/T
Integrate[dS, {S1, S2}]=Integrate[dQ/T, {T2, T}]
S|{S1, S2} = Integrate[M*c*dT/T, {T2, T}]
S2 - S1 = M*cp*m*Integrate[dT/T, {T2,T}]
Delta-S = M*cp*Ln[T]|{T2, T}
Delta-S = M*cp*Ln[T/T2]
Delta-S = Ro*V*Ln[T/T2]

If we insert numbers...

Delta-S = 963 J/K (this one is positive, so the entropy of air increased).


Since I don't need to account for change from water vapor to water, I can use the same formula to calculate the change of entropy of water.

Delta-S = m*c*Ln[T1/T]
Delta-S = 845 J/K (again, positive)

So the total Delta-S of the system is 1808 J/K.


So yea........ things aren't always as they seem to be.

We've seen that even though water COOLED down, it's entropy still increased. The reason is that the natural state of heat is that it flows from hot to cold... hot -> cold increases entropy.

Good calculating.
Hot -> cold increases entropy and decreases enthalpy
cold -> hot decreases entropy and increases enthalpy (right?)
and because I can decrease the entropy in a own system by putting energy/work into.

 

[RisingFury]

Now let's look at a simple fridge. We'll assume that the fridge is 100% efficient, converting all of the energy it receives from electricity into cooling and we'll assume the fridge is perfectly insulated so no heat is able to get inside it.

We have 1 kg of air inside the fridge at 20°C and we want to cool it down to -20°C. Now let's look at how much entropy of such a system changes:

m = 1 kg
c = 1 kJ/(kg*K)
Delta-T = 40K
-----------------
Delta-S = ?


The energy the fridge will need to cool the air is equal to the heat it needs to extract:

A = Q
Q = m*c*Delta-T
A = m*c*Delta-T = 40 000J

And the entropy change?

Delta-S = m*c*Ln(T2/T1) = -147 J/K

See, the entropy is negative, but to get it lower, we had to use a 40 000 J.

So the easiest conclusion from this is that when heat flows naturally from hot to cold, the entropy increases, but when we have to force heat to flow from cold to hot, the entropy decreases... but we have to pay for the decrease with work.