The exhaust temperature is 200 K
Explanation:
The maximum efficiency of a machine is given by the equation:
[tex]\eta=1-\frac{T_C}{T_H}[/tex]
where:
[tex]T_H[/tex] is the temperature of the hot reservoir
[tex]T_C[/tex] is the temperature of the cold reservoir
For the engine in this problem, we have:
[tex]\eta = 0.333[/tex] (efficiency is 33.3%)
[tex]T_H=300K[/tex] is the temperature of the hot reservoir
Re-arranging the equation for [tex]T_C[/tex], we can find the exhaust temperature (the temperature of the cold reservoir):
[tex]T_C=T_H(1-\eta)=(300)(1-0.333)=200 K[/tex]
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