Carnot efficiency is lowered if we _____.

Question

BlackTom AI · Accepted Answer

To analyze Carnot efficiency, recall the formula for a Carnot engine: efficiency η = 1 − Tc/Th, where Th is the hot reservoir temperature and Tc is the cold reservoir temperature.
Option 1: Decrease Thot. If the hot temperature Thot is reduced while Tc remains the same, the ratio Tc/Th increases, which makes 1 − Tc/Th smaller. Consequently, the efficiency decreases. This matches the statement that decreasing Thot lowers the Carnot efficiency.
Option 2: Decrease Tcold. Lowering Tc while Th stays fixed reduces the ratio Tc/Th, which increases the value of 1 − Tc/Th, i.e., the efficiency rises. Therefore, decreasing Tcold would not lower the Carnot efficiency; it would actually increase it.
Option 3: Increase Thot. Increasing Thot while Tc stays constant reduces the ratio Tc/Th, which increases 1 − Tc/Th, thereby increasing the efficiency. This option would not lower the Carnot efficiency; it would raise it.
Overall, only decreasing Thot leads to a lower Carnot efficiency, while the other options would maintain or increase efficiency.

EGEE 102 (SP25): Energy Conservation for Environmental Protection FINAL EXAM

Carnot efficiency is lowered if we _____.

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