# Cascade Carnot cycle

In a Carnot cycle about 50% of the energy is converted in work whereas the other is dissipated in heat to the heat sources.

Is it possible to reuse the heat in another cycle to reconvert 50% of it into work?

If so, it would theoretically be possible to eventually convert all the initial energy into work since :

$\underset{n=1}\Sigma (\frac{1}{2})^n = \frac{1}{1-\frac{1}{2}}-1=1$ .

However, I fell this is not possible since only the free energy F = U-TS of the original gas should be convertible into work.

• "In a Carnot cycle about 50% of the energy is converted in work whereas the other is dissipated in heat to the heat sources." Why 50%? – noah Aug 18 '17 at 17:09
• To do this, you need to have subsequent cycle heat sinks at lower and lower temperatures. How far do you think you have such heat sinks available? – Chet Miller Aug 18 '17 at 17:31
• @noah it is about 50% the exact theoretical value being $\eta = 1-\frac{T_c}{T_h}$ where $T_h$ and $T_c$ are the heat source constant temperatures. – Ronan Tarik Drevon Aug 19 '17 at 14:11
• I know the efficiency of the Carnot cycle, but why would you assume that the hot bath is twice as hot as the cold one? – noah Aug 19 '17 at 14:14
• @ChesterMiller that's a good point. Indeed, 3 or 4 stages already bring the temperature of the cold source very low. In practice, though how many stages are being used? – Ronan Tarik Drevon Aug 19 '17 at 14:17