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Starting from any given corner, the first two sides of the loop can be as long or short as you like, and then after that the last two sides have to be just the right length in order that the loop can close using just two isothermal and two adiabatic parts in total. It's a bit like making a rectangle (well it is a lot like making a rectangle if you plot the ...

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Why does adiabatic contraction bring Carnot engine back to initial state? The short answer is the work done on the gas during the adiabatic compression has to increase the internal energy of the gas by the same amount that the adiabatic expansion reduced the internal energy of the gas, so that the total change in internal energy of the cycle is zero. Keep ...

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I only know a long ride for this, sorry :/ You have to imagine two processes iabf and if that have the same work $\Delta W_{iabf}=\Delta W_{if}$: (Dashed lines are adiabatic curves and solide lines are isothermes) The internal energy variation is the same for both processes and $\Delta Q_{ab}=\Delta Q_{if}$. Now imagine a system S' that provides energy $\... 1 Here is a very simple derivation from 1961,see Penfield ! Start with the picture of a Carnot engine sandwiched between two thermal resistances each being attached to a thermostat. According to Carnot's efficiency theorem the work$W$delivered $$W \le \big(1-\frac{T_2}{T_1}\big)Q \tag{1}\label{1}$$ where$Q\$ is the heat entering the engine at the higher ...

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