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Energy pumps and the second law
Renewable Energy 30 (2005) 1127–1131 www.elsevier.com/locate/renene
Technical note
Energy pumps and the second law R.C. Mathews (Retired) Unit 55 The Grange, 2 McAuley Place, Waitara, NSW 2077, Australia Received 31 May 2004; accepted 14 September 2004 Available online 21 December 2004
The Second Law of Thermodynamics states ‘The entropy of a closed system can never decrease’. Scientists express this law in many different ways: † Energy cannot be recycled and do work. † The Clausius statement ‘It is impossible for a self acting machine, unaided by an external agent, to convey heat from one body to another’ † Energy transformation must increase entropy. This paper examines the thermodynamics of the Stirling engine, chilled with liquid nitrogen, and the novelty toy, the continually drinking duck (inventor unknown but available in toy shops for at least the last forty years). The analysis shows that: † The Stirling engine is a heat engine that recycles ambient heat and does work. The chilled nitrogen entropy increases. † The duck is an isentropic energy pump that upgrades and recycles ambient energy and does work. The driver—evaporating water entropy increases. † The duck energy pump and driver do not suffer Carnot efficiency losses. The duck is a controllable energy pump, but it only releases micro amounts of low entropy energy. The weather system is an energy pump and it releases massive amounts of low entropy energy, but it is uncontrollable except for certain locations, where low entropy hydropower and wind power is recovered. The energy pump concept provides an incentive for research to determine if controllable, practical energy pumps can be developed. The Second Law is universal, but the analysis shows that some of the scientists’ expressions of this law are not universal. The operating cycle of the Stirling engine, with liquid nitrogen, is well known. The chilled gas from the heat sink is recycled into the operating chamber, where it absorbs 0960-1481/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2004.09.005
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ambient heat; the gas expands, does work and is exhausted into the heat sink. The work energy is recycled into the pool of ambient heat and can do more work. The liquid nitrogen chills the exhaust gas and its entropy increases. An increase in entropy is also experienced in the manufacture of liquid nitrogen. The Stirling engine is a typical Carnot cycle heat engine with a direct temperature relationship between the heat source and the heat sink. The drinking duck is similar to the Stirling engine in that it absorbs ambient heat, converts it into work and recycles it back into the pool of solar energy. It also has an artificial ‘heat sink’—evaporating water. This is where the similarity ends; it has a completely different operating cycle to that of the Stirling engine. The drinking duck is made of glass with the head covered in felt, the body is a glass tube and the base of the duck is a bulb, which contains liquid freon. It balances on a swivel at its midpoint. Water added to the duck’s head evaporates (depending on atmospheric humidity) and changes the freon in the duck from a stable condition to a condition of non-equilibrium. The head is cooled due to the latent heat of vaporisation of the water. This reduces the vapour pressure of the freon in the head. The higher vapour pressure of the freon in the bulb, at the base of the duck, causes liquid freon to flow from the base to the head via the body tube. When the freon reaches a certain level it will cause the duck to be in a state of imbalance and the head will dip into a beaker of water, this maintains the felt head wet, a pin stops the duck from completing a full circle. The liquid freon in the tube returns to the base and displaces the vapour which returns to the tube. Observation shows that the base of the duck is the dry bulb temperature (Tdb) and the head of the duck is the wet bulb temperature (Twb). This temperature differential suggests a Carnot cycle heat engine with a direct flow of energy from the base to the head of the duck. However, the operating cycle of the drinking duck does not conform with a Carnot cycle heat engine. The cycle sequence is as follows: † Evaporating water, cools the freon vapour in the head. † The reduced pressure in the head (due to the cooling) is transmitted, via the vapour and liquid in the tube, to the base. † This sets off a series of energy transformations in the base: free expansion of freon vapour, cooling due to free expansion of freon vapour, evaporation of liquid freon, cooling due to latent heat of evaporation of freon, absorption of ambient heat, an increased head of freon in the tube and work is done. † At the end of the cycle liquid freon returns to the base of the drinking duck, the vapour in the base replaces the liquid in the tube. Observation shows that ambient heat enters the base of the duck via the liquid from the tube as well as from the base. Ambient heat enters the head of the duck via the vapour in the tube. At no stage during the cycle does cooled vapour, from the head, enter the base of the duck (cooled vapour is not available until after the first cycle). Also freon vapour from the expansion cycle does not directly enter the head of the duck (vapour replaces liquid in the tube). There is no direct relationship between the dry bulb temperature at the base of the duck and the wet bulb temperature at the head of the duck. This operating cycle is unrelated to a Carnot cycle heat engine. It shows that the evaporating water, and the accompanying reduced pressure in the head, is driving the energy transformation in
R.C. Mathews / Renewable Energy 30 (2005) 1127–1131
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the base. This results in (1) an upgrade of ambient energy to low entropy energy, a head of freon (2) a downgrade of the head of freon as it does work, and its entropy increases (3) the work energy returns to the pool of ambient energy and it can be recycled to do more work. The net result is that there is no increase in entropy of the ambient energy that does work. This leads to the conclusion that the drinking duck is an ‘energy pump’. Evaporating water cools the vapour in the head and its entropy increases. What is an ‘energy pump’? It is suggested that an energy pump is analogous to a heat pump. Heat pumps have a driver that upgrades and recycles heat. Energy pumps have a driver that upgrades and recycles energy. As will be shown later, energy pumps have the potential to be self-driven, whereas, heat pumps do not have this potential. Heat pumps and energy pumps have a Coefficient of Performance (CoP) at least equal to one or greater. A CoP less than one would not energy balance. For illustration purposes assume the duck energy pump has a CoPZ1.0. Also assume that over a given time period 100 units of energy are absorbed as latent heat of evaporation at the duck’s head—say Q3Z100 units of energy. Q1 is the energy absorbed at the duck’s base and Q2 is the energy released by the duck operation. Refer to Fig. 1. CoPZ Q2 =ðQ2 K Q1 Þ, Q3ZQ2KQ1Z100, 1.0ZQ2/100, Q2Z100, Q1Z0. That is, if the CoPZ1.0 then the duck operation is based on a direct transfer of energy from the evaporating water to the energy absorbed at the base of the duck. However, due to the cooling of freon caused by evaporation and free expansion (the pressure reduction in the base of the duck is analogous to the free expansion and cooling of gases that rise in the atmosphere) the base absorbs ambient energy. This increased energy input results in a CoP greater than one. Heat pumps upgrade and recycle heat without any change in entropy, energy pumps upgrade and recycle energy without any change in entropy, that is, they are isentropic. The duck CoP is probably only a fraction greater than one but for illustration purposes assume the CoPZ5. The following calculation shows that an energy pump with a CoP greater than one would not violate the First and Second Laws of Thermodynamics. If the equivalent amount of potential energy, of liquid freon in the tube, had been released as heat, its temperature can be calculated by using the temperature equation for heat pumps: i.e. CoPZT2/T2KT1 assume T1Z20 8C or 293 K. If the CoPZ5, Q1Z400, Q2Z500 and T2Z366.25 K or 93.25 8C. The entropy of the energy absorbed equals the entropy of the energy released, i.e. Q1/T1ZQ2/T2 or 400/293Z500/366.25 or 1.36Z1.36. The energy of the system is also in balance with a CoP of 5.0, viz: Energy input by driver (duck’s head). Q3Z100 Plus energy absorbed at duck’s base Q1Z400 Equals energy released by duck Q2Z500
Fig. 1. Duck as energy pump.
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The total energy of the system is not affected by the duck operation, it is a simple transfer of energy in exactly the same way that a heat pump transfers energy. The following conclusions can be made from the duck operation: † The duck is driven by evaporating water, and based on the availability of water, it will continue to operate until the earth reaches maximum entropy. † The duck is in a continual state of non-equilibrium, which causes it to recycle indirect solar energy as high entropy energy into low entropy energy, a head of freon, and do work. † The duck operates with a CoP greater than 1.0 and it does not violate the first and second laws of thermodynamics. † The duck driver does not suffer Carnot efficiency losses and the potential energy from the head of freon does not suffer Carnot efficiency losses when doing work. That is ‘the duck is a controllable, naturally driven energy pump, which recycles high entropy energy at ambient temperatures into low entropy energy, a head of freon, does work and does not suffer Carnot efficiency losses’. This leads to the conclusion: that there are no theoretical constraints preventing the development of a self-driven energy pump, if the energy for the driver and the energy produced are the same type of energy and that the energy does not suffer Carnot efficiency losses when doing work. An example is an electrical driven energy pump, which converts energy at ambient temperatures into electrical energy. Physical phenomena do exist, that have this potential; if placed in a state of non-equilibrium, but the final outcome will only be determined by research work. Although there are no theoretical constraints preventing the development of a selfdriven energy pump, numerous attempts to develop such a machine have failed. As a result, a number of formulations of the second law of thermodynamics have been made, which are best summarized by the Clausius statement. Which states ‘it is impossible for a self acting machine, unaided by any external agent, to convey heat from one body to another at a higher temperature’. The Clausius statement is applicable to heat engines, which require a low entropy energy fuel to drive them. It is also applicable to the drinking duck, which requires an external force (evaporating water) to drive it. But there is a fundamental difference between the energy, which does work by a heat engine, and the energy, which does work by an energy pump. Heat engines suffer Carnot efficiency losses, whereas energy pumps (such as the drinking duck) do not incur Carnot efficiency losses. It is for this reason that it is both theoretically and practically impossible to develop a self-driven heat engine but theoretically possible to develop a self-driven energy pump. The second law of thermodynamics simply states ‘the entropy of a closed system can never decrease’. Energy pumps, such as the drinking duck, recycle high and low entropy energy and do work i.e. energy pumps are isentropic which means that theoretically a selfdriven energy pump would not violate the second law of thermodynamics. However, in practice, experience has shown that entropy is always increasing and is a clearly defined ‘arrow of time.’ The entropy increase of low entropy energy, which drives heat engines, is finite in time. Whereas, energy pumps such as the drinking duck are isentropic, but they are still subject
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to the ‘arrow of time’ because of the entropy increase due to erosion and corrosion of the duck and the indirect solar energy they recycle is increasing in entropy over time. The duck will cease recycling energy when the earth reaches maximum entropy. The duck driver, evaporating water, will continue to operate over the same time scale. A self-driven energy pump would also be constrained to the same time scale, which is consistent with the observation that entropy is always increasing. The weather system is a self-driven energy pump that is driven by the non-equilibrium of the vapour pressure of water and the partial vapour pressure of water in the atmosphere. Water is continually evaporating by absorbing high entropy indirect solar energy. The weather system releases massive amounts of low entropy energy, but this energy cannot be controlled except for some fixed locations, where low entropy energy is recovered as wind power and hydropower. The duck releases micro amounts of low entropy energy, as a head of freon, but it is controllable and versatile and it can operate in many locations in the world. The energy pump concept provides an incentive to determine if—practical, controllable, energy pumps can be developed.
Technical note
Energy pumps and the second law R.C. Mathews (Retired) Unit 55 The Grange, 2 McAuley Place, Waitara, NSW 2077, Australia Received 31 May 2004; accepted 14 September 2004 Available online 21 December 2004
The Second Law of Thermodynamics states ‘The entropy of a closed system can never decrease’. Scientists express this law in many different ways: † Energy cannot be recycled and do work. † The Clausius statement ‘It is impossible for a self acting machine, unaided by an external agent, to convey heat from one body to another’ † Energy transformation must increase entropy. This paper examines the thermodynamics of the Stirling engine, chilled with liquid nitrogen, and the novelty toy, the continually drinking duck (inventor unknown but available in toy shops for at least the last forty years). The analysis shows that: † The Stirling engine is a heat engine that recycles ambient heat and does work. The chilled nitrogen entropy increases. † The duck is an isentropic energy pump that upgrades and recycles ambient energy and does work. The driver—evaporating water entropy increases. † The duck energy pump and driver do not suffer Carnot efficiency losses. The duck is a controllable energy pump, but it only releases micro amounts of low entropy energy. The weather system is an energy pump and it releases massive amounts of low entropy energy, but it is uncontrollable except for certain locations, where low entropy hydropower and wind power is recovered. The energy pump concept provides an incentive for research to determine if controllable, practical energy pumps can be developed. The Second Law is universal, but the analysis shows that some of the scientists’ expressions of this law are not universal. The operating cycle of the Stirling engine, with liquid nitrogen, is well known. The chilled gas from the heat sink is recycled into the operating chamber, where it absorbs 0960-1481/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2004.09.005
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R.C. Mathews / Renewable Energy 30 (2005) 1127–1131
ambient heat; the gas expands, does work and is exhausted into the heat sink. The work energy is recycled into the pool of ambient heat and can do more work. The liquid nitrogen chills the exhaust gas and its entropy increases. An increase in entropy is also experienced in the manufacture of liquid nitrogen. The Stirling engine is a typical Carnot cycle heat engine with a direct temperature relationship between the heat source and the heat sink. The drinking duck is similar to the Stirling engine in that it absorbs ambient heat, converts it into work and recycles it back into the pool of solar energy. It also has an artificial ‘heat sink’—evaporating water. This is where the similarity ends; it has a completely different operating cycle to that of the Stirling engine. The drinking duck is made of glass with the head covered in felt, the body is a glass tube and the base of the duck is a bulb, which contains liquid freon. It balances on a swivel at its midpoint. Water added to the duck’s head evaporates (depending on atmospheric humidity) and changes the freon in the duck from a stable condition to a condition of non-equilibrium. The head is cooled due to the latent heat of vaporisation of the water. This reduces the vapour pressure of the freon in the head. The higher vapour pressure of the freon in the bulb, at the base of the duck, causes liquid freon to flow from the base to the head via the body tube. When the freon reaches a certain level it will cause the duck to be in a state of imbalance and the head will dip into a beaker of water, this maintains the felt head wet, a pin stops the duck from completing a full circle. The liquid freon in the tube returns to the base and displaces the vapour which returns to the tube. Observation shows that the base of the duck is the dry bulb temperature (Tdb) and the head of the duck is the wet bulb temperature (Twb). This temperature differential suggests a Carnot cycle heat engine with a direct flow of energy from the base to the head of the duck. However, the operating cycle of the drinking duck does not conform with a Carnot cycle heat engine. The cycle sequence is as follows: † Evaporating water, cools the freon vapour in the head. † The reduced pressure in the head (due to the cooling) is transmitted, via the vapour and liquid in the tube, to the base. † This sets off a series of energy transformations in the base: free expansion of freon vapour, cooling due to free expansion of freon vapour, evaporation of liquid freon, cooling due to latent heat of evaporation of freon, absorption of ambient heat, an increased head of freon in the tube and work is done. † At the end of the cycle liquid freon returns to the base of the drinking duck, the vapour in the base replaces the liquid in the tube. Observation shows that ambient heat enters the base of the duck via the liquid from the tube as well as from the base. Ambient heat enters the head of the duck via the vapour in the tube. At no stage during the cycle does cooled vapour, from the head, enter the base of the duck (cooled vapour is not available until after the first cycle). Also freon vapour from the expansion cycle does not directly enter the head of the duck (vapour replaces liquid in the tube). There is no direct relationship between the dry bulb temperature at the base of the duck and the wet bulb temperature at the head of the duck. This operating cycle is unrelated to a Carnot cycle heat engine. It shows that the evaporating water, and the accompanying reduced pressure in the head, is driving the energy transformation in
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the base. This results in (1) an upgrade of ambient energy to low entropy energy, a head of freon (2) a downgrade of the head of freon as it does work, and its entropy increases (3) the work energy returns to the pool of ambient energy and it can be recycled to do more work. The net result is that there is no increase in entropy of the ambient energy that does work. This leads to the conclusion that the drinking duck is an ‘energy pump’. Evaporating water cools the vapour in the head and its entropy increases. What is an ‘energy pump’? It is suggested that an energy pump is analogous to a heat pump. Heat pumps have a driver that upgrades and recycles heat. Energy pumps have a driver that upgrades and recycles energy. As will be shown later, energy pumps have the potential to be self-driven, whereas, heat pumps do not have this potential. Heat pumps and energy pumps have a Coefficient of Performance (CoP) at least equal to one or greater. A CoP less than one would not energy balance. For illustration purposes assume the duck energy pump has a CoPZ1.0. Also assume that over a given time period 100 units of energy are absorbed as latent heat of evaporation at the duck’s head—say Q3Z100 units of energy. Q1 is the energy absorbed at the duck’s base and Q2 is the energy released by the duck operation. Refer to Fig. 1. CoPZ Q2 =ðQ2 K Q1 Þ, Q3ZQ2KQ1Z100, 1.0ZQ2/100, Q2Z100, Q1Z0. That is, if the CoPZ1.0 then the duck operation is based on a direct transfer of energy from the evaporating water to the energy absorbed at the base of the duck. However, due to the cooling of freon caused by evaporation and free expansion (the pressure reduction in the base of the duck is analogous to the free expansion and cooling of gases that rise in the atmosphere) the base absorbs ambient energy. This increased energy input results in a CoP greater than one. Heat pumps upgrade and recycle heat without any change in entropy, energy pumps upgrade and recycle energy without any change in entropy, that is, they are isentropic. The duck CoP is probably only a fraction greater than one but for illustration purposes assume the CoPZ5. The following calculation shows that an energy pump with a CoP greater than one would not violate the First and Second Laws of Thermodynamics. If the equivalent amount of potential energy, of liquid freon in the tube, had been released as heat, its temperature can be calculated by using the temperature equation for heat pumps: i.e. CoPZT2/T2KT1 assume T1Z20 8C or 293 K. If the CoPZ5, Q1Z400, Q2Z500 and T2Z366.25 K or 93.25 8C. The entropy of the energy absorbed equals the entropy of the energy released, i.e. Q1/T1ZQ2/T2 or 400/293Z500/366.25 or 1.36Z1.36. The energy of the system is also in balance with a CoP of 5.0, viz: Energy input by driver (duck’s head). Q3Z100 Plus energy absorbed at duck’s base Q1Z400 Equals energy released by duck Q2Z500
Fig. 1. Duck as energy pump.
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R.C. Mathews / Renewable Energy 30 (2005) 1127–1131
The total energy of the system is not affected by the duck operation, it is a simple transfer of energy in exactly the same way that a heat pump transfers energy. The following conclusions can be made from the duck operation: † The duck is driven by evaporating water, and based on the availability of water, it will continue to operate until the earth reaches maximum entropy. † The duck is in a continual state of non-equilibrium, which causes it to recycle indirect solar energy as high entropy energy into low entropy energy, a head of freon, and do work. † The duck operates with a CoP greater than 1.0 and it does not violate the first and second laws of thermodynamics. † The duck driver does not suffer Carnot efficiency losses and the potential energy from the head of freon does not suffer Carnot efficiency losses when doing work. That is ‘the duck is a controllable, naturally driven energy pump, which recycles high entropy energy at ambient temperatures into low entropy energy, a head of freon, does work and does not suffer Carnot efficiency losses’. This leads to the conclusion: that there are no theoretical constraints preventing the development of a self-driven energy pump, if the energy for the driver and the energy produced are the same type of energy and that the energy does not suffer Carnot efficiency losses when doing work. An example is an electrical driven energy pump, which converts energy at ambient temperatures into electrical energy. Physical phenomena do exist, that have this potential; if placed in a state of non-equilibrium, but the final outcome will only be determined by research work. Although there are no theoretical constraints preventing the development of a selfdriven energy pump, numerous attempts to develop such a machine have failed. As a result, a number of formulations of the second law of thermodynamics have been made, which are best summarized by the Clausius statement. Which states ‘it is impossible for a self acting machine, unaided by any external agent, to convey heat from one body to another at a higher temperature’. The Clausius statement is applicable to heat engines, which require a low entropy energy fuel to drive them. It is also applicable to the drinking duck, which requires an external force (evaporating water) to drive it. But there is a fundamental difference between the energy, which does work by a heat engine, and the energy, which does work by an energy pump. Heat engines suffer Carnot efficiency losses, whereas energy pumps (such as the drinking duck) do not incur Carnot efficiency losses. It is for this reason that it is both theoretically and practically impossible to develop a self-driven heat engine but theoretically possible to develop a self-driven energy pump. The second law of thermodynamics simply states ‘the entropy of a closed system can never decrease’. Energy pumps, such as the drinking duck, recycle high and low entropy energy and do work i.e. energy pumps are isentropic which means that theoretically a selfdriven energy pump would not violate the second law of thermodynamics. However, in practice, experience has shown that entropy is always increasing and is a clearly defined ‘arrow of time.’ The entropy increase of low entropy energy, which drives heat engines, is finite in time. Whereas, energy pumps such as the drinking duck are isentropic, but they are still subject
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to the ‘arrow of time’ because of the entropy increase due to erosion and corrosion of the duck and the indirect solar energy they recycle is increasing in entropy over time. The duck will cease recycling energy when the earth reaches maximum entropy. The duck driver, evaporating water, will continue to operate over the same time scale. A self-driven energy pump would also be constrained to the same time scale, which is consistent with the observation that entropy is always increasing. The weather system is a self-driven energy pump that is driven by the non-equilibrium of the vapour pressure of water and the partial vapour pressure of water in the atmosphere. Water is continually evaporating by absorbing high entropy indirect solar energy. The weather system releases massive amounts of low entropy energy, but this energy cannot be controlled except for some fixed locations, where low entropy energy is recovered as wind power and hydropower. The duck releases micro amounts of low entropy energy, as a head of freon, but it is controllable and versatile and it can operate in many locations in the world. The energy pump concept provides an incentive to determine if—practical, controllable, energy pumps can be developed.