- #1
zenterix
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- Homework Statement
- I am reading the book "Heat and Thermodynamics" by Zemansky and Dittman. Chapter 6 entitled "The 2nd Law of Thermodynamics" starts with multiple sections on heat engines and then on the refrigerator.
- Relevant Equations
- My question is about dissipative effects. Before I get to my question, which has to do with the 2nd law of thermodynamics, I want to go through some of the topics presented in the chapter before the section on dissipative effects.
There is a statement of the 2nd law by Kelvin-Planck
and then a statement of the 2nd law by Clausius
Then, it is shown that these statements are equivalent. This is done by showing the following (this is how I understood it, anyways)
a) If the Clausius statement is false, then we can make a refrigerator that extracts ##|Q_L|## from a cold reservoir without requiring any work. We can use this heat in the cycle of a heat engine: ##|Q_L|## goes into its cold reservoir and ##|Q_H|## is extracted from its hot reservoir such that ##|Q_H|-|Q_L|## of work is done on its surroundings. Thus, such a refrigerator together with the heat engine constitutes a form of perpetual motion machine (of the second kind): in a cycle, ##|Q_H|## is extracted from the hot reservoir, work is done on the surroundings, but there is no net rejection of heat to the cold reservoir. This violates the Kelvin-Planck statement.
b) If the Kelvin-Planck statement is false, then we can make a heat engine that extracts ##|Q_H|## from its hot reservoir without rejecting any heat to the cold reservoir. The associated work can be used in the cycle of a refrigerator: compression of the refrigerant in the isothermal compression part of its cycle, with ##|Q_H|## going into its hot reservoir. ##|Q_L|## is removed from its cold reservoir. Taken together, the refrigerator and the heat engine constitute a form of perpetual motion machine (of the second kind): in a cycle, ##|Q_L|## of heat is removed from the cold reservoir but no net heat into the hot reservoir. This violates the Clausius statement.
Then there is a discussion on reversibility and irreversibility.
Finally, we reach the part that I have some major questions about.
There is a large class of processes involving the isothermal transformation of work through a system (which remains unchanged) into internal energy of a reservoir. This type of process is depicted schematically in the following figure
Five examples of this type of process are
1) Friction from rubbing two solids in contact with a reservoir.
2) Irregular stirring of a viscous liquid in contact with the reservoir.
3) Inelastic deformation of a solid in contact with the reservoir.
4) Transfer of charge through a resistor in contact with the reservoir.
5) Magnetic hysteresis of a material in contact with the reservoir.
In order to restore the system and its local surroundings to their initial states without producing changes elsewhere, ##|Q|## units of heat would have to be extracted from the reservoir and converted completely into work. Since this would involve a violation of the second law (Kelvin statement), all processes of the above type are irreversible.
Let's consider just the first example.
Take two stones, one in each hand, submerge the stones in water (a cold reservoir) and start rubbing them together. We are performing mechanical work which is somehow being converted into heat that is passing into the water.
To restore the stones and local surroundings to their initial states without producing changes elsewhere, we would have to extract heat from the water and convert it completely into work.
I don't quite understand what it would mean to convert the heat to work in this example with the stones.
In terms of violating the second law, it seems we would have to be able to devise a machine that would extract heat from the reservoir (now a hot reservoir) and completely turn this into work without rejecting any heat, thus violating the 2nd law (in particular as it is stated by Kelvin-Planck.
The essence here seems to be that we can dissipate heat when we perform work but we can't recover the heat completely.
In other words, we can dissipate work freely, but we can't extract heat freely (as this would violate the 2nd law and imply the possibility of perpetual motion machine).
Is this a correct interpretation of the topics above?
and then a statement of the 2nd law by Clausius
Then, it is shown that these statements are equivalent. This is done by showing the following (this is how I understood it, anyways)
a) If the Clausius statement is false, then we can make a refrigerator that extracts ##|Q_L|## from a cold reservoir without requiring any work. We can use this heat in the cycle of a heat engine: ##|Q_L|## goes into its cold reservoir and ##|Q_H|## is extracted from its hot reservoir such that ##|Q_H|-|Q_L|## of work is done on its surroundings. Thus, such a refrigerator together with the heat engine constitutes a form of perpetual motion machine (of the second kind): in a cycle, ##|Q_H|## is extracted from the hot reservoir, work is done on the surroundings, but there is no net rejection of heat to the cold reservoir. This violates the Kelvin-Planck statement.
b) If the Kelvin-Planck statement is false, then we can make a heat engine that extracts ##|Q_H|## from its hot reservoir without rejecting any heat to the cold reservoir. The associated work can be used in the cycle of a refrigerator: compression of the refrigerant in the isothermal compression part of its cycle, with ##|Q_H|## going into its hot reservoir. ##|Q_L|## is removed from its cold reservoir. Taken together, the refrigerator and the heat engine constitute a form of perpetual motion machine (of the second kind): in a cycle, ##|Q_L|## of heat is removed from the cold reservoir but no net heat into the hot reservoir. This violates the Clausius statement.
Then there is a discussion on reversibility and irreversibility.
Finally, we reach the part that I have some major questions about.
There is a large class of processes involving the isothermal transformation of work through a system (which remains unchanged) into internal energy of a reservoir. This type of process is depicted schematically in the following figure
Five examples of this type of process are
1) Friction from rubbing two solids in contact with a reservoir.
2) Irregular stirring of a viscous liquid in contact with the reservoir.
3) Inelastic deformation of a solid in contact with the reservoir.
4) Transfer of charge through a resistor in contact with the reservoir.
5) Magnetic hysteresis of a material in contact with the reservoir.
In order to restore the system and its local surroundings to their initial states without producing changes elsewhere, ##|Q|## units of heat would have to be extracted from the reservoir and converted completely into work. Since this would involve a violation of the second law (Kelvin statement), all processes of the above type are irreversible.
Let's consider just the first example.
Take two stones, one in each hand, submerge the stones in water (a cold reservoir) and start rubbing them together. We are performing mechanical work which is somehow being converted into heat that is passing into the water.
To restore the stones and local surroundings to their initial states without producing changes elsewhere, we would have to extract heat from the water and convert it completely into work.
I don't quite understand what it would mean to convert the heat to work in this example with the stones.
In terms of violating the second law, it seems we would have to be able to devise a machine that would extract heat from the reservoir (now a hot reservoir) and completely turn this into work without rejecting any heat, thus violating the 2nd law (in particular as it is stated by Kelvin-Planck.
The essence here seems to be that we can dissipate heat when we perform work but we can't recover the heat completely.
In other words, we can dissipate work freely, but we can't extract heat freely (as this would violate the 2nd law and imply the possibility of perpetual motion machine).
Is this a correct interpretation of the topics above?