Explain how real machines can never recover the full amount of energy they were supplied with?.
1 Answer
Sounds like efficiency to me. In general, efficiency is defined as the work output acquired from some work input.
where:
#w# is work.#q_H# is the heat flow into the engine from the hot reservoir.#q_C# is the heat flow from the engine into the cold reservoir.#T_H# is the temperature of the hot reservoir.#T_C# is the temperature of the cold reservoir.
The ideal machine can achieve
As I derived above, a cyclic process has a change in entropy of
If we separate the cyclic process into two processes, then
#q_H/T_H + q_C/T_C = 0#
Also from the above, I calculated that
#color(blue)(e) = |w|/q_H = (q_H + q_C)/q_H = color(blue)(1 + q_C/q_H)# .
Or, using the first relation:
#color(blue)(e) = |w|/q_H = (q_H + q_C)/q_H = color(blue)(1 - T_C/T_H)# .
So, we could even say that since all absolute temperatures are positive (i.e. when in
Therefore, the efficiency can never be more than