22. Maximum value the efficiency of a heat engine

In 1824, the French engineer Nicolas Léonard Sadi Carnot, in his book "Reflections on the Motive Power of Fire", proved that when the work done by some heat taken from the heater at temperature \( T_1 \), part of the heat was given to the fridge at a lower temperature \( T_2 \). It was subsequently shown that the efficiency of any thermal engine cannot exceed some maximum value. It was then shown that the efficiency of any thermal engine cannot exceed some maximum value

\( \eta_{max} = \frac{T_1 - T_2}{T_1} \)

As an example, let's define the upper limit of possible values of efficiency of a steam turbine. Typical for a steam turbine initial and final steam temperatures \( T_1 = 800^0 K \) and \( T_2 = 300^0 K \).

At these values

\( \eta_{max} = \frac{T_1 - T_2}{T_1} \times 100\% \approx 62\% \)

Because of the different energy losses, the actual efficiency is \( \eta \approx 40\% \).

It would seem that the efficiency of the turbine can be increased by increasing the temperature of steam \( T_1 \). However, the possibility of increasing efficiency in this way is limited by the insufficient heat resistance of the turbine blade material.