- #1
Soren4
- 128
- 2
The thermal engine efficiency is defined as
$$\eta = \frac{W_{\mathrm{produced}}}{Q_{\mathrm{absorbed}}}\tag{1}$$
A more general definition of efficiency (not only for thermal machines is) $$\eta = \frac{\mathrm{Work \, produced}}{\mathrm{Energy \, absorbed}}\tag{2}$$
But suppose that, in one of the processes that takes place in the cycle of an engine that works with an ideal gas, work is supplied to the gas, for istance with a fan delivering a certain power. That work is not a "boundary work" but it is supplied to the system by the fan.
That work of the fan (say ##W_{\mathrm{fan}}##) is a form of energy that must be supplied in order to make the engine work, so should it be taken into account in the efficiency? That is should I write, in that case, $$\eta = \frac{W_{\mathrm{produced}}}{Q_{\mathrm{absorbed}}+W_{\mathrm{fan}}}\,?\tag{3}$$
It makes sense but often the definition of efficiency is just ##(1)##, the only thing in denominator is heat and not work. So is ##(3)## the correct form for efficiency for such situations?
$$\eta = \frac{W_{\mathrm{produced}}}{Q_{\mathrm{absorbed}}}\tag{1}$$
A more general definition of efficiency (not only for thermal machines is) $$\eta = \frac{\mathrm{Work \, produced}}{\mathrm{Energy \, absorbed}}\tag{2}$$
But suppose that, in one of the processes that takes place in the cycle of an engine that works with an ideal gas, work is supplied to the gas, for istance with a fan delivering a certain power. That work is not a "boundary work" but it is supplied to the system by the fan.
That work of the fan (say ##W_{\mathrm{fan}}##) is a form of energy that must be supplied in order to make the engine work, so should it be taken into account in the efficiency? That is should I write, in that case, $$\eta = \frac{W_{\mathrm{produced}}}{Q_{\mathrm{absorbed}}+W_{\mathrm{fan}}}\,?\tag{3}$$
It makes sense but often the definition of efficiency is just ##(1)##, the only thing in denominator is heat and not work. So is ##(3)## the correct form for efficiency for such situations?