Heat, temperature and gravity Emil Junvik

Transcription

1 Heat, temperature and gravity Emil Junvik Abstract A simple analysis of planetary temperatures and the relationship between heat flow and gravity in spherical shells. It includes equations for electric fields and global formulations of the first law of thermodynamics for Earth, Mars and Venus. A single equation is shown to be able to produce σt 4 at 1 bar pressure for all three planets. The energy-mass equivalence is used as a base for connecting gravity to Earth surface temperature. By simplifying flows of energy on a global scale, all observed heat flows and the force of gravity are exactly balanced and quantized. Keywords: planteary theory, planetary temperature, heat transfer, electric field equations, gravity 1. Introduction In this manuscript I analyze heat flow and force on a global scale in an extremely simplified setting where I reduce the system to only heat and work, based on potentials in temperature differences and transformations from geometry in spherical shells. I also show that equations used for electricity is well suited for heat and work in this setting. Without assumptions and using only known principles based on proven theories and laws, I show that heat transferred according to potentials in temperature, show exact relationships in all three inner planets. I also show how the physical quantities used by Einstein in his equation for mass-energy equivalence, leads us directly to a connection between earth surface temperature and gravity. This is also connected to the concept of gravitational charge by using an equation for uniform charge inside a sphere, where solar irradiation shows an exact correlation to gravity on a global scale. Adding the equation for the work done in a capacitor, where TSI is connected to a thermal capacitans which relates to the stored energy necessary to drive the gravitational acceleration continously, confirms the usefulness of electrodynamics when describing planetary energy balance.

2 When doing this work it has been problematic to get feedback from people working in the field. The response has been practically non-existent. Bejan and Reis ( Thermodynamic optimization of global circulation and climate, 005 doi.org/10.100/er.1058 ) propose an approach to analyzing the climate system using the constructal law that can be applied to thermodynamic flows of energy. In the theory flows evolves into maximum dissipation of the power from the heat source over time in a steady state. The constructional theory says that flow under natural conditions will do work on matter towards optimized flow effiency. I use the ideal case with only geometric constrictions to represent a state with optimized heat flow inside the system, connected to solar irradiance at TOA. The results seems to match reality with high accuracy. Since this manuscript only uses known, proven and applied principles and laws of physics with publicly available data, I will not give any other references except for Adrian Bejans paper on the constructal theory. From beginning to end this analysis was done based on only the Stefan-Boltzmann equation for emissive power, σt 4, and simplified geometric ratios in an ideal setting. This work is independent and it was produced outside of academic institutions..1 The modified blackbody model of earth T SI = W /m σ = 5.67 * 10 8 I start by taking a look at the differences between the two-dimensional spherical surface of the absorbing and emitting blackbody, and the three-dimensional volume of Earth absorbing solar radiation. To find the emitted intensity of the surface of the inner spherical shell, we need to account for absorption over πr from the received intensity from solar irradiation, TSI, over the disc that is the shadow of earth, πr. Then we need to account for absorption in depth in a volume of 4πr 3 /3 within the system. Two shells of concentric volumes need to be accounted for. Atmosphere and solid earth, which gives: ( T SI * π r )/(πr 3 3 )/(4πr /3) = ( 4πr /3) * 3 83W /m (1) I am only interested in the rate of change in each point, so I simplify this into: 1 / * T SI/(4/3) = 383W /m Which is equal to a surface temperature of 86.6 Kelvin. This is very close to the average temperature given in the literature, which often is said to be 87-88K. This Equation, in this simplified form, surprisingly produces σt 4 for Earth, Mars and Venus at 1 bar pressure. Hereafter V=4/3.

3 Using irradiation at TOA and surface temperature result to find the potential of maximum heat transfer: 1 T SI T SI/V = 978W /m Irradiation must be treated as a point source if connected to spherical effective emission: () 1 1/4(T SI T SI/V ) = 44.5W /m Taking a closer look at the process where heat from the sun reach the surface, we find a correlation to equatorial surface irradiation at zenith: T SI/V = W /m With TSI and effective temperature there is a potential heat transfer to the system, with a precise correlation to observed equatorial total solar irradiation, including both direct and diffuse radiation: (4) T SI σt 4 effective = 1 116W /m We now have a basic structure of the system determined by only small modifications of the blackbody concept in potentials of heat transfer from average temperatures and observed levels of irradiation, combined with basic principles like the inverse square law. I want to direct attention to the difference between the emitted effective temperature, and the true blackbody temperature of a perfect absorber and emitter, irradiated at the level of TSI. Per unit surface area, a blackbody would absorb and emit: T SI/4 = 340.W /m The difference to observed effective temperature is: (6) ( T SI/4) σt 4 effective = 95.7W /m The first law of thermodynamics tells us that a closed system with added energy U will have an internal relationship U = Q W, where Q is the heat flow into the low temperature reservoir (space), W is the work done on the system. With average irradiation as U and effective temperature as Q, the work done on the system is: (5) (3) (7) U(T SI/4) Q (44.5) = W (95.7) (8) The globally observed work done in the earth system is the force of gravity, displacing mass. Since both U and Q are dimensioned as P/A, we need to change gravity s action from linear force into pressure/stress. Using the value of equatorial surface acceleration from NASA s earth fact sheet: U(T SI/4) Q (44.5) = W (g ) (9) We know that N/m = W /m, so the relationship between irradiation and the lever arm vector producing torque of gravity in a fixed point, is: (T SI/4) 9.78N/m.78W /m (10) σt 4 effective = = 9 The power of the pressure of gravity is:

4 A force equal to g ( T SI/4) σt 4 effective = 9 5.7N/m = 95.7W /m (11) acting at the surface of a sphere must have a source power of: 4((T SI/4) σt 4 effective ) = 383W /m (1) In terms of source power, the first law is: U(T SI) = 4 W + 4 Q (13) Looking at the internal relationships between temperatures in terms of emissive power, we can see that: and σt 4 surface = 3 4 σt tropopause σt 4 surface = 4 σt 4 tropopause 4 3 (14) (15) From this I build an equation of state that is the same as for a fluid: σt surface = 4 g 4 + g 3 = T SI/8/3 (16). The modified blackbody model of Mars It not that easy to find conclusive data on Mars temperature distribution as for earth, but insolation is given by NASA fact sheet for Mars, which should be reliable. A common value for surface mean temperature is 18K. According to the observed effective temperature is 1K. The website gives a slightly higher value of insolation than NASA. Since the solar constant for earth has been corrected from 1370W /m to W /m not that long ago, I will use the lower value given by NASA. NASAs fact sheet for Mars gives a blackbody temperature of 10K, which in this case is used instead of effective temperature. The real blackbody temperature, though, would be 5K, since a blackbody absorbs and emit all radiation from the heat source. TSI: 586W /m Surface temperature: 18K, 18W /m Blackbody Effective Temperature: 5K, 146.5W /m Observed Effective Temperature: 09.8K, 109.8W /m With the same method as in chapter.1., using potential radiative heat transfer with TSI as a point source: T SI σt 4 surface = 4 4 σt effective (17) From that we find that effective temperature should be 1K which is equal to emissive power of 114.5W /m slightly higher than observation, 09.8K.

5 And, we also find that 1 / * T SI/(4/3) gives the temperature at one 1 bar pressure, but this point is below the surface since surface pressure is only 0.6 bar. Surface acceleration torque used as pressure is same relationship as on earth: ( T SI/4) σt 4 effective = 3 W /m g = 13.6,and g ravity does not show the (18) On Mars, the first law is not balanced in surface acceleration and effective emission. Using a single shell for absorption with TSI as a point source, we instead find that the effective emission given by NASA has the correlation: 1 /4 * ( T SI/V ) = 8g = 109.8W /m = 09.8K Instead, the potential heat transfer to the whole system, from TSI and effective emission, shows a relationship in the first law as: (19) U(T SI) = 4 /3(3Q + 8 W ) = 4/3(3σT 4 effective + 8 g ) (0) Here I found no other solution than to include the ratio of volume to surface area in the first law, which is not necessary for Earth and Venus. TSI can also be balanced by only heat emission or only gravity: 4 /3 * 4 Q = 4 /3 * 3g (1).3 The modified blackbody model of Venus TSI: 601W /m Surface temperature: ~740K Effective temperature: 6.6K g = 8.87 On Venus the surface has a very high temperature which can not be explained by direct heat from the sun since very little sunlight reach all the way down. Using only the geometrical relationships, there is an approximate correlation: 4 (T SI/V 3 ) = 1755W /m = 745K () Solar irradiation and surface emission is clearly not balanced at the solid surface. But the heat flows shows other relationships. The equation 1 / * T SI/(4/3) correctly gives σ T at one bar pressure, 50km altitude, at 337K. The difference between the emissive power of the perfect blackbody and the emissive power of Venus effective temperature is: And there is also a correlation: ( T SI/4) σt 4 effective = 500W /m 4 (3)

6 T SI ( T SI/4) = T SI/V (4) There is an exact correlation between gravity and effective emission: T SI = 4 W + 16Q (5) We can also see a relationship T SI/V = 4g. g is here slightly above what s calculated from it s mass, 9.016/8.87, and possibly g could be shown to be the higher value if measured on Venus..4 Energy-mass equivalence, physical quantities and useful electric concepts Einstein revealed a relationship between the inertia of mass and the energy in usually referred to as E = mc. In the equation E = mc E/c = m, more we find the physical quantities m=kg and c=m/s. The unit newton, N, used for forces, is k g * m /s. So Einstein was literary describing a force/inertia in newtons, E = N = k g(m/s)². Since the original formula was E /c² = m, he was describing the energy of mass in terms of the force equal to inertia in newtons as E/c = N /(m/s)² = k g. Some people appear to disagree with my interpretation of E as a force, but since Einstein dealed with the inertia of bodies, I see no problem with this, given the results below. Gravity on earth is defined in newton as N = k g * 9.8m/s, the exact same physical quantities as as in E = mc². This means that E = N = k g * 9.8(m/s) and E/v = 9.8N/(m/s) = k g. Remembering that N/(m/s)=J/(m/s)=W/m, then E/v E = g ² = 9.8²N/(m/s)² = 96N/m² = 96W /m The force of gravity, g², acting on 1m² has the power 96W /m². According to the inverse square law the source power is 4g = 4 * 96W /m² = 384W /m² (7) This is equal to the average surface temperature of earth at 87K. The relationship to Einsteins E/c = m is (6) has a clear representation in the state of our planet. Earth with the mass m receives Solar heat at the speed c and simultaneously emits heat at the speed c Seeing that in all directions. 4g = σt 4 surface, and introducing the concept of a charged sphere: Then it is easy to see that: T SI/8g² = ( 4/3)/(4/3) (8)

7 This implies that Einsteins energy-mass equivalence can be used for a planet in space, where E = mc² actually is a mass placed in a radiation field with incoming heat at speed c, while simultaneously emitting heat at speed c. Earth, in terms of thermal energy, can apparently be reduced to the same equations as a spherical conductor in an electric field. By replacing electrical charge with high intensity solar radiation and coupling it to the force of gravity, there is an obvious equality where the inertia from E/c global state appears as N/(m/s) =g, which can be seen as the gravitational unit of charge in a T SI/(4/3) = 4 /3 * 8g (9) Another electrical concept which comes to mind when considering energy and work, is a capacitor. The capacitor consists of two conductors with opposing surfaces separated by a dielectric medium. To charge the capacitor, work has to be done by an external force which moves the charge against the potential which determines the direction of force in the electric field. If the distance between the surfaces is constant, the electric field will be constant and can be determined by the volume of the field. For a capacitor with capacitance C, the work done in moving a charge Q is W = 1/CV. The potential V is defined as a hollow sphere with a concentric conductor, and in the case of capacitance the volume of the field determines the work done in creating the charge. The potential V is 4πr 3 /3. The capacitance is then

8 C = W /V = 8g /V (30) And W = 1/CV = 1/ΔU/V (31) where Δ U = T SI. Not only is there a clear connection between heat, gravity and electric concepts, the thermal and electric concepts of power, potential and work have analogies in hydraulics and hydrodynamics. A simple example is the reduced equation of state for a fluid, can be used with solar irradiation to show that: 8 /3T, which T SI/(8/3) = 4/3 * σt 4 surface = 4 g + 4/3g (3) That an equation for fluids works so well for heat flow from temperature potentials, imply that light/heat is actually fluid..5 Total solar irradiance, T 4 and the Stefan-Boltzmann constant As a peculiar sidenote, in the calculations I initially used a value of TSI at 1361W /m. When using the exact mean value given by NASA, W, I noticed a surprising detail. When using the Stefan-Boltzmann constant, 5.67 * 1 0 8, to convert watt to temperature, I found that T 4 (T SI) = This gives even numbers throughout the equations for earth. σ is actually * 1 0 8, but we don t have that precision of measurements of TSI. T SI T 4 surface T 4 effective T 4 tropopause g Conclusions & Discussion In this article, the extreme simplifications into idealized conditions in a steady state is initially based on the minimalistic relationships in optimization of a heat engine. The radiation entering from vacuum is connected to the body s effective emission to vacuum, but also includes an underlaying structure of detailed balance between heat and work. The constructal law and the calculations made here, supports an approach where a new focus on old physics could produce answers to long standing questions, like the problem of earth surface temperature and the force of gravity.

9 The average addition to terrestrial surface emission from internally generated heat is commonly known to be only 90mW /m. Almost all energy above surface is then considered to be solar energy, or related only to TSI, which is a large simplification. I support this on the idea of the surface being in equilibrium (no net heat transfer), based on the tiny net geothermal heat flow of 90mW /m. The model makes no assumptions of hidden or unknown sources of energy, not even for the force of gravity. It accounts for all energy and work in terms of heat emission based on temperature distribution. Borrowing concepts from electric field theory shows that global heat flow and work done by/on the system easily can be described by well known and applied models for energy and work. By using the first law of thermodynamics, all three inner planets can easily be given a global energy balance including only heat and work. The exact match of Earth mean temperatures and inclusion of gravity, makes a far better job than earlier theories of planetary temperatures which use a concept of heat-trapping. The surprising finding that 1 / * T SI/(4/3) gets temperature correctly at 1 bar pressure for the three planets further supports the idea that there is a better way to an energy balance than the greenhouse theory. Further analysis of other planets and the internal relationships within the solar system should be of interest, confirming or refuting this approach to temperature and/or gravity. It seems unlikely that the relationships shown in this paper is purely coincidence, although it seems necessary to adapt the model to local differences from observations. I suspect that the planets beyond Mars will show entirely different relationships with solar irradiation. Nevertheless, I believe they will also behave as idealized/optimized cases.