Answer:
[tex]\eta=\frac{W}{Q_{c}}\\\\ \eta=\frac{Q_{c}-Q_{f}}{Q_{c}}[/tex]
Explanation:
We have the expression for a heat engine as:
[tex]Q_{c}=W+Q_{f}[/tex]
Where Qc is the hot source, or the energy that the engine receives, W is the work produced by the engine and Qf is the heat that is delivered to a cold spot.
If we have a 100% efficiency, all the energy that the engine receives turns into output work, so Qf is zero, therefore, from the original expression we can define a formula for efficiency:
[tex]\eta=\frac{W}{Q_{c}}[/tex]
Now, by doing some algebra, we can have the following expression:
[tex]\eta=\frac{Q_{c}-Q_{f}}{Q_{c}}[/tex]
That also can be expressed as:
[tex]\eta=1-\frac{Q_{f}}{Q_{c}}[/tex]
