Consider a big Carnot cycle. It's 100% reversible -- as efficient as you can get. No losses. And it's 100% reversible no matter what temperature it operates at.
The amount of energy out/energy in is T_h/T_c = 1.
This is a 100% efficient energy storage system. It is also our idealized cycle -- a gigantic, single Carnot cycle, storing energy in heat and in low entropy, highly compressed air.
Now, the Carnot efficiency, or the efficiency of a heat engine, is a completely different kind of efficiency. It's the TOTAL energy out divided by the heat in. This is
(W_out-W_in)/Q_in
In our case, the Carnot efficiency is zero, even though the cycle is reversible, and the energy storage process is completely reversible.
Interesting indeed, and thanks for the reply. I almost understand it, unfortunately I just returned from our Melbourne Cup party, where lots of wine was consumed. For now, I concede that your concept seems theoretically possible, best of luck!
The Carnot cycle is:
1. Isothermal compression (T_c) 2. Adiabatic compression (T_c -> T_h) 3. Isothermal expansion (T_h) 4. Adiabatic expansion. (T_h -> T_c)
The adiabatic compression and expansion processes are just to get between the two temperatures, T_hot and T_cold.
Suppose T_hot = T_cold.
Then there's no adiabatic section, and it's just
1. Isothermal compression (T) 2. Isothermal expansion (T)
The amount of energy out/energy in is T_h/T_c = 1.
This is a 100% efficient energy storage system. It is also our idealized cycle -- a gigantic, single Carnot cycle, storing energy in heat and in low entropy, highly compressed air.
Now, the Carnot efficiency, or the efficiency of a heat engine, is a completely different kind of efficiency. It's the TOTAL energy out divided by the heat in. This is
(W_out-W_in)/Q_in
In our case, the Carnot efficiency is zero, even though the cycle is reversible, and the energy storage process is completely reversible.
Interesting, no?