In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal efficiency of that cycle will be $$\eta=1-\frac{T_{\mathrm{min}}}{T_{\mathrm{max}}}.$$

As noticed by Wolphram jonny, the sentence above is not true. The Carnot theorem states that any reversible engine operating between two reservoirs has the maximum efficiency given by the equation above. So the only possible cycle between two sources is the Carnot cycle.

It does not mean that you cannot have other reversible cycles. However these cycles would not represent a thermal engine operating between two reservoirs.

For the cycle you drew, there are two possibilities. Either it has two sources and then its efficiency would be less than the Carnot efficiency, which means it is not an irreversible. Or it is reversible which means it has infinite sources. Each source is in thermal equilibrium with a small portion of the cycle.

In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal efficiency of that cycle will be $$\eta=1-\frac{T_{\mathrm{min}}}{T_{\mathrm{max}}}.$$

As noticed by Wolphram jonny, the sentence above is not true. The Carnot theorem states that any reversible engine operating between two reservoirs has the maximum efficiency given by the equation above. So the only possible reversible cycle between two sources is the Carnot cycle.

It does not mean that you cannot have other reversible cycles. However these cycles would not represent a thermal engine operating between two reservoirs.

For the cycle you drew, there are two possibilities. Either it has two sources and then its efficiency would be less than the Carnot efficiency, which means it is not an irreversible. Or it is reversible which means it has infinite sources. Each source is in thermal equilibrium with a small portion of the cycle.

In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal efficiency of that cycle will be $$\eta=1-\frac{T_{\mathrm{min}}}{T_{\mathrm{max}}}.$$

As noticed by Wolphram jonny, this sentence above is not true. The Carnot theorem states that any reversible engine operating between two reservoirs have the maximum efficiency as given by the equation above. So the only cycle possible between two sources is the Carnot cycle.

It does not mean you cannot have other reversible cycles. However these cycles would not represent a thermal engine operating between two reservoirs.

For the cycle you drew, there are two possibilities. Either it has two sources and then its efficiency would be less than the Carnot efficiency, which means it is not a reversible engine. Or it is reversible which means it has infinite sources. Each source is in thermal equilibrium with a small portion of the cycle.

In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal efficiency of that cycle will be $$\eta=1-\frac{T_{\mathrm{min}}}{T_{\mathrm{max}}}.$$

As noticed by Wolphram jonny, the sentence above is not true. The Carnot theorem states that any reversible engine operating between two reservoirs has the maximum efficiency given by the equation above. So the only possible cycle between two sources is the Carnot cycle.

It does not mean that you cannot have other reversible cycles. However these cycles would not represent a thermal engine operating between two reservoirs.

For the cycle you drew, there are two possibilities. Either it has two sources and then its efficiency would be less than the Carnot efficiency, which means it is not an irreversible. Or it is reversible which means it has infinite sources. Each source is in thermal equilibrium with a small portion of the cycle.