FuelScience.org offers more theories of Heat Engines, a respectful addendum to the work of past physicists.

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Additional theorems.
These are believed to be original, but no exhaustive search was done.

Commentary

Note ambient heat is equal on intake and exhaust, and does not affect work, nor does it affect the amount of fuel needed.

Theorems and Corollaries

Corollary FS-1: An optimal Heat Engine will diffuse or disburse no Fuel Heat.

Proof is Carnot's Theorem that diffusion is waste. An optimal engine has no waste, so cannot dissipate fuel heat in any form.

We distinguish Fuel Heat from ambient heat, because a heat engine always dissipates ambient heat if it intakes and exhausts any vapor.

It is generally understood that compressing air is a means of storing energy, which is true and yet misleading. If the compressed air had no heat, no energy would be stored.

There are compressed air vehicles, powered by air compressed to several hundred atmospheres. The process of compression includes discarding the heat generated, which is the vast majority of the work intended to be stored. So at first glance this would appear an extremely inefficient process. However, as air is released, it does work and is cooled as is the storage tank. The Atmosphere replenished the heat, holding it at near ambient temperature. So effectively, this method makes use of the atmosphere (the pressure envelope) to store most of the energy.

If compression were only done on very cold days, and the tanks used on very hot days, there is even some gain to the process!

Theorem FS-1: Where there is a vapor pressure difference, a heat engine may be made, whether or not there is a temperature. difference:

Proof is simple, a pressure difference can directly create work via Volume change. This will consume heat, whether or not any temperature. existed to begin with.

This can be considered the dual to Carnot's axiom that wherever there is a temperature. difference, a motive force can be made.

Roughly 3 categories of Heat engines exist.

  1. Uncooled Heat Engines
  2. Cooled Heat Engines
  3. Recycling Heat Engines

There is a direct correspondence between the heat engine types and the 3 cases in this corollary.

Theorem FS-2: A heat engines Work to Fuel Heat ratio is its Fuel Efficiency. Its Work Ratio is 1 minus the Heat Ratio, where the Heat Ratio is determined by Volume Expansion Ratio. The math of Heat dissipation is such that:

  1. If the engine dissipates unconverted Fuel Heat, its Fuel Efficiency ratio will be the Work Ratio for the Engines volume expansion ratio. This has been historically claimed an inherent limit.
  2. If the machine exhausts, dissipates or diffuses more heat than its heat ratio, it is effectively leaking heat. This heat is prevented from becoming work. All heat engines with any type of cooling system whatsoever fall into this category. These engines will apparently consume more heat, than the (Work divided by the Heat Ratio) plus Exhaust heat. Conversely, the Work produced will be less than the Initial Heat times the Work Ratio. Its Fuel Efficiency will be less than its Work ratio by a factor determined by the amount of "cooling" aka "Leaking heat" is done.
  3. A heat Engine that exhausts no heat, will have a Fuel efficiency of 100%, matching the natural energy conversion efficiency between heat and work. The Work Ratio in such a case is independent of the efficiency, although must be non zero.

This is not a proof that another solution does not exist. It is a statement of a possible and feasible solution to the problem posed by asymmetric conversion.

Theorem FS-3: The condition necessary for 100% heat conversion (and a necessary condition for 100% Fuel efficiency) is met by a heat recycling engine.

Proof: Due to asymmetric energy conversion, volume expansion converts a portion of heat to work, and leaves an unconverted portion. The unconverted portion must be recycled to reach 100% heat conversion, in the steady state. Using the heat in a future cycle reduces the required fuel heat in the same future cycle at a ratio of one to one. This allows no heat to be exhausted. The engine will never convert the initial remainder, which will also be the final heat remainder.

Example: A 1 to 10 expansion typical car engine, will have all heat added before expansion. Should some heat be added beginning before expansion, and continuing till half way through expansion, (as in Carnot Cycle) The heat added at the end will experience a 1 to 2 expansion and the rest of the heat will experience up to a 1 to 10 expansion. The effective average will be in the middle. So less total Work will be done by "Carnot heating" as compared to "Automotive heating".

Theorem FS-4: The maximum Work Ratio for an engine cycle with a given expansion ratio requires all heat to be added before any expansion.

Proof: Any heat added after expansion begins, will encounter less than the engine's expansion ratio, so will have a greater Heat Ratio for that portion of the heat, and a lesser Work Ratio for that portion of the heat. The total effective Work Ratio will be a weighted average of the Heat Ratio summed for each quantity of heat added.

This does not imply there are no advantages to uninsulated or isothermal compression, nor that insulated compression is best. It just defines the conditions for maximum work area from an insulated compression.

However, a combination of isothermal and insulated compression (Carnot Cycle) within a single volume cycle has no advantages over either.

Theorem FS-5: Achieving the maximum Work Area (Pressure times Volume change) for a given engine cycle which does insulated (or adiabatic) compression, requires all disbursed heat to be removed before before any compression.

Proof: This is the dual to previous theorem. The lowest possible compression curve yields the greatest area of work. So, since the work curve's shape is fixed by the vapor's constant exponent, the greatest area above the curve is achieved by starting the curve at the lowest point. Removing heat later in the cycle would raise the compression work curve.

As stated in chapter Three Laws, this concept is not new. However, it appears to be a fundamental property of Thermodynamics.

That is, measurement of temperature depends on frame of reference of motion. Methodology of measurement may need to be adjusted accordingly. For example, wind temperature, where velocity is high, hurricanes, or temperature is low, arctic.

Theorem FS-6: Temperature is Relative

Proof: Consider a gas whose molecules have an average velocity Vrandom, and a smaller velocity, Vwind. In both cases, consider only the vector towards the Thermometer body.

Molecules will strike a thermometer, measuring average momentum. Energy of Momentum is proportional to velocity squared.

Molecules with a net 0 or negative net velocity will not strike. Molecules with specific Vrandom less than Vwind, will strike, but would not have without Vwind (more molecules will strike, because of Vwind). Molecules with maximum specific VRandom toward the thermometer body will strike with velocity VRandom+Vwind. So the average velocity of molecules striking thermometer body is increased by somewhere between Vwind/2 and Vwind.

More molecules will contact, the maximum speed is higher, the minimum speed unchanged.

The only comment here, should this be considered over-obvious, is that there is a widespread belief that thermodynamic efficiency depends on high temperatures.

Efficiency is determined by relative changes, and by preserving the energy in the system. A system can be made as efficient operating from 200 below zero or 2000 above, if they operate over the same ratio of change.

Theorem FS-7: Thermodynamic conversions of vapors are relative.

Proof: The proof is that this is simply a property of an exponential curve, which defines the relation between temperature/heat, pressure, and volume. Any relative change on the curve in x or y coordinate, yields the same proportional change in the opposite coordinate.

Thermodynamic conversions of vapors are relative to a starting point, and independent of absolute temperature, volume or pressure. In vapor phase, the ratios of relative changes are always the same.

The absolute volume, temperature, pressure, are independent of the system behavior for the same relative changes.