Question

What temperature is required to transfer waste heat to the environment for a heat engine to be 100 percent efficient?

Answer 1

This can be seen as a trick question because heat engines can typically never be 100 percent efficient. This is due to the presence of inefficiencies such as friction and heat loss to the environment. Even the best heat engines can only go up to around 50% efficiency.

Answer 2

Answer:

An infinite temperature

Explanation:

The efficiency of an engine is defined as:

$\eta=1 -\frac{T_C}{T_H}$

where

$T_H$ is the temperature at which heat enters the engine

$T_C$ is the temperature of the environment, to which the engine exhausts heat

From the formula, we see that for an engine to be 100% efficient, the fraction

$\frac{T_C}{T_H}$

must be equal to zero. Since the value of $T_C$ is never zero (the temperature is expressed in Kelvin, and the temperature of the environment can never be exactly 0 K), the only possibility for that to occur is that the temperature at which heat enters the engine ($T_H$) is infinite, so that this fraction becomes zero and the efficiency becomes 1.