# Is this interpretation of 2nd law of Thermodynamics correct?

1. Sep 21, 2009

### superkan619

Suppose A box represents the universe. It also has a battery and a propellor inside it. The propellor is supposed to increase the temperature of the whole universe including itself and the battery.

If this hypothetical universe is initially at 25 degrees C, then we incresed this temp to 27 deg C. This means that we've converted work into heat at the given (initial) temp of 25 deg C. This is allowed by 2nd law.

But if we were to consider converting the initial heat of universe into work (upon the propellor) at given (initial) temp of 25 deg C so that the universal temp finally falls to 23 deg C, it would be rendered impossible by 2nd law.

Are the above interpretations correct??

2. Sep 21, 2009

### superkan619

From the statement of 2nd law of thermodynamics, I meant to ask:

Is it that, throught the process of conversion of heat into work or work into heat, the system's+surrounding's temp must be at a single temperature?

OR

the initial temperature of system+surrounding must be constant before we can begin conversion of heat to work or vice versa?

3. Sep 21, 2009

### jambaugh

No and No.

In order to convert heat into work it must flow from higher temperature to lower temperature (increasing entropy). In your example the energy is conserved. The energy stored in the battery is at low entropy. When it is used to turn the motor and generate heat it increases entropy.

Be careful about thinking either that "hotter" or "colder" represents "higher entropy". Entropy is not equal to temperature or it would be called "temperature". When energy is changed from some stored form to heat the entropy goes up and the temperature goes up. When a hot system contacts a cold system the heat energy flows to the cold side until the temperatures equalize. Again the entropy is going up.

If you want to think in terms of constancy of temperatures consider a heat-pump instead of your motor-propeller. Cut your "universe" into too halves and let the battery pump heat from one side to the other. The heat pump may act also as a heat engine and recharge the battery as the heat flows back through. However when the temperatures equalize again the total temp will be a bit higher and the battery a bit less charged.

4. Sep 21, 2009

### jambaugh

5. Sep 21, 2009

### superkan619

IInd law states that "It is impossible to convert heat back into work at a given temperature". Can you please explain me properly the meaning of "at" i.e is it the initial temp of sys+surr or temp of sys+surr throught the process of conversion.

What I think is that, it is physically impossible to maintain a constant temp throught the process of conversion of heat into work, so this is meaningless. Hence initial temp statement is what we need to ask Mr Carnot, which he would reply in negative.

Last edited: Sep 21, 2009
6. Sep 21, 2009

### superkan619

7. Sep 22, 2009

### jambaugh

In order to convert heat to work it must flow from a higher temperature system to a lower temperature system.
How that breaks down i.e. whether it is a difference in temperature between system and surroundings or whether it is a matter of temperature of distinct modes (hot e-m radiation vs cold atoms) is immaterial.
No that's not the point. You are trying to invoke a non-existent causation.

I'll give you the long winded speech now on the subject...

In one sense the 2nd law is like Newton's 3rd law. All interactions between systems are two-way. For example if an atom can emit radiation then radiation can kick the atom around.

This means that when two systems interact randomly there will be a tendency for their energy to be passed back and forth until it is equally distributed between all the physical degrees of freedom. The average energy per degree of freedom is what defines temperature. (This is called the equipartition principle) The average energy per degree of freedom is what defines temperature.

Two systems at different temperatures when allowed to interact will start randomly exchanging energy but again it will tend to flow on average from hotter to cooler until the two systems reach equal intermediate temperatures. By the 2nd Law there can be no one-way coupling (a Maxwell's daemon) which only allows energy to pass one way and thereby increasing the temperature difference.

Now the idea of "doing useful work" involves putting a great deal of energy into a single degree of freedom. For example in a piston engine the energy of the random 3-dimensional motions of all the gas atoms gets partially converted to the uniform motion of all the atoms of the piston in one direction.

In this example and relevant to your last point you can allow the expanding gas to push the piston but stay at a constant temperature by injecting heat as it expands. The conversion process itself doesn't need a difference in temperature. Rather the process of injecting that heat must either be due to heat flowing in from a higher temperature reservoir or (as in the case of an internal combustion engine) through the conversion of other stored energy into heat.

Finally to convert heat to energy on a continuous basis (we can't just let the piston continue to go forward indefinitely.) the heat being injected must be dissipated as well. Only some of it can be converted to work.

So in the abstract if you have a device for converting heat to work it must be taking heat from a higher temperature source and dissipating heat to a lower temperature source and along the way some of that heat energy is redirected into the work channel.

It is not that the conversion of heat to work causes a change in temperature but rather that the only cause for a conversion of heat to work is a difference in temperature.

8. Sep 22, 2009

### superkan619

Carnot assumed that heat cannot be taken in (i.e consumed)at a certain temperature and converted to work with no other change in the system or surrounding.