Reversible Processes: Isothermal to Adiabatic Transition

[AirForceOne]

The problem:
A red-hot 2.00 kg piece of iron at temperature t1=880k is thrown into a huge lake whose temperature is t2=280K. Assume the lake is so large that its temperature rise is insignificant.

The book says that this process is irreversible. Why?

I have another question. In a reversible process, are the initial and final state variables (p,v,T,Eint,S) the same? Or is does that only true for a cycle? I'm really confused haha. If all the processes in a carnot cycle are reversible, how come the temperature changes when going from the isothermal to adiabatic process, even though the process is done very slowly? How come that process is not irreversible?

Thanks.

 

[Drakkith]

You could not reverse the process and transfer all that heat back into the iron without doing work. IE the heat would not spontaneously flow back from the cooler lake into the warmer iron. That is why it is not reversible.

 

[Andrew Mason]

You could not reverse the process and transfer all that heat back into the iron without doing work. IE the heat would not spontaneously flow back from the cooler lake into the warmer iron. That is why it is not reversible.

Heat will not flow back from the cooler lake to the warmer iron, true. But that is not why it is not reversible. It would not flow back from the cooler lake to the warmer iron in a reversible process either. A reversible process still requires work to reverse. It is just that the amount of work is required to reverse it is the same as the amount of work generated in the forward process.

A reversible path between the two states would be achieved by connecting a Carnot heat engine between the iron and the lake until the lake and iron are at virtually the same temperature (ie. arbitrarily close to the same temperature). The work generated could be stored (say, by lifting a weight or spinning a flywheel). Then the heat could be taken out of the lake and transferred back to the iron (theoretically) by making an infinitessimal change in the relative temperatures of the iron/lake and running the heat engine in reverse as a Carnot heat pump using the stored energy. The work required for the heat pump to move that heat back would be arbitrarily close to the energy that was stored from the output of the Carnot heat engine.

AM

 

[Andrew Mason]

I have another question. In a reversible process, are the initial and final state variables (p,v,T,Eint,S) the same? Or is does that only true for a cycle? I'm really confused haha.

The final state variables are not the same as the initial. For the iron, obviously temperature and entropy change. The temperature for the lake does not change but the entropy does (it increases).

If all the processes in a carnot cycle are reversible, how come the temperature changes when going from the isothermal to adiabatic process, even though the process is done very slowly? How come that process is not irreversible?

The temperature change is reversible because the isothermal and adiabatic processes can be reversed with an infinitessimal change in conditions and by supplying back the work that was generated in the forward process.

AM

 

[Studiot]

The definition of a reversible process provides a simple test for reversibility.

A reversible process is one in which all intermediate states are equlibrium states.

Now when the hot iron is thrown into the lake is it in (thermal) equilibrium?

 

[elasticities]

Whats an example of a reversible physical change not at equilibrium?

 

[Andrew Mason]

Whats an example of a reversible physical change not at equilibrium?

A reversible physical change requires processes that are quasi-static. A quasi-static process means that it occurs while everything is in equilibrium (ie. out of equilibrium by an infinitessimal amount). So, there are no such examples.

AM

 

[elasticities]

A reversible physical change requires processes that are quasi-static. A quasi-static process means that it occurs while everything is in equilibrium (ie. out of equilibrium by an infinitessimal amount). So, there are no such examples.

AM

Really?

Like a chemical process not at equilibrium would be a open can of pop...

 

[Andrew Mason]

Really?

Like a chemical process not at equilibrium would be a open can of pop...

Not sure what your point is.

AM

 

[elasticities]

Not sure what your point is.

AM

But isn't evaporation of a puddle after rain a physical change that is not at equilibrium?

Also is an open bottle of carbonated beverage (like a 2L bottle) an example of a chemical change not at equilibrium?

 

[Andrew Mason]

But isn't evaporation of a puddle after rain a physical change that is not at equilibrium?

Also is an open bottle of carbonated beverage (like a 2L bottle) an example of a chemical change not at equilibrium?

Yes. But these are not reversible processes. A reversible process is one whose direction can be reversed by an infinitessimal change in conditions: ie. a process that occurs while arbitrarily close to equilibrium.

AM