So why struggle to post 'obscure symbols" when it would obviously be a simple matter to post the correct, universally accepted and well understood equation?
Internal energy is not temperature. For a gas, internal energy and temperature are related but not the same thing. Saying that "internal energy is... temperature" is just wrong.The point here is internal energy is vibrations, temperature. Heat is not. All equations clearly separate them, even when you quote them.
Q is a quantity of energy in Joules, W is a quantity of energy in Joules.
Temperature is not a quantity, it's an average. A 16 ounce glass of water at 100°C does not contain the same quantity of energy as as a five gallon pot of boiling water at 100°C
Temperature is not a quantity of energy.
If you add 300 joules of heat or work to a model LTD you are not going to bring the working fluid temperature up the same number of degrees that you would adding the same 300 joules of work or heat to a 25 kilowatt engine.
Temperature is not joules of energy.
Heat, work and internal energy are all measured in Joules because fundamentally they ARE all the same thing: energy.
Temperature is not an actual quantity of energy.
You happily and with complete abandon substitute 300 joules for 300 degrees in your various attempts at your "derivation". As above, you are careless about your notation. Qez Qcz etc. just making stuff up without clear definitions.
The more complicated you make it the easier it is to pull a "switcheroo" which even Matt Brown called you out on.
So when VincentG writes you a blank check saying: "... the math is sound. Things can be computed accurately, that can't be denied"
Sorry but math can easily be fouled up, misapplied, misunderstood, screwed around with and deliberately abused in a thousand different ways and should always be checked and rechecked and compared with reality through empirical experiment, not just given Carte blanche, especially when dealing with "fool" and his IMO, intentionally deceptive "derivations". and number juggling in general.
If a mathematical derivation and empirical experimental results don't agree, guess who wins?
If experimental results don't conform to some 200 year old efficiency formula that was based on a fallacious theory of heat and has never been empirically tested or verified I think it's perfectly justified to question the mathematical formula that repeatedly resulted in wrong predictions for experimental outcomes.