The maximum amount of work performed is
[tex]W_{max}=\frac{T_H-T_C}{T_C}Q_C[/tex]
Explanation:
The efficiency of a real heat engine is given by the equation:
[tex]\eta = 1-\frac{T_C}{T_H}[/tex] (1)
where
[tex]T_C[/tex] is the temperature of the cold reservoir
[tex]T_H[/tex] is the temperature of the hot reservoir
However, the efficiency of a real heat engine can be also written as:
[tex]\eta = \frac{W_{max}}{Q_H}[/tex]
where
[tex]W_{max}[/tex] is the maximum work done
[tex]Q_H[/tex] is the heat absorbed from the hot reservoir
[tex]Q_H[/tex] can be written as
[tex]Q_H=W_{max}+Q_C[/tex]
where
[tex]Q_C[/tex]is the heat released to the cold reservoir
So the previous equation can be also written as
[tex]\eta=\frac{W_{max}}{W_{max}+Q_C}[/tex] (2)
By combining eq.(1) and (2) we get
[tex]1-\frac{T_C}{T_H}=\frac{W_{max}}{W_{max}+Q}[/tex]
And re-arranging the equation and solving for [tex]W_{max}[/tex], we find
[tex]W_{max}=\frac{T_H-T_C}{T_C}Q_C[/tex]
Learn more about work and heat:
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