Question

A real heat engine operates between temperatures Tc and Th. During a certain time, an amount Qc of heat is released to the cold reservoir. During that time, what is the maximum amount of work Wmax that the engine might have performed? Express your answer in terms of Qc, Th, and Tc.

Answer 1

Answer:

$W_{max} =Q_C(\dfrac{T_H}{T_C} - 1)$

Explanation:

given,

Temperature of heat engine operate between

Th (temperature in hot reservoir) and Tc(temperature in cold reservoir)

amount of heat released to = Qc

to find maximum amount of work = ?

now,

efficiency of heat engine

$\eta = 1 - \dfrac{T_C}{T_H} = 1 -\dfrac{Q_C}{Q_H}$

now,

$\dfrac{T_C}{T_H} = \dfrac{Q_C}{Q_H}$

$Q_H= \dfrac{T_H}{T_C} Q_C$

 maximum work =

$W_{max} = Q_H - Q_C$

$W_{max} =\dfrac{T_H}{T_C} Q_C - Q_C$

$W_{max} =Q_C(\dfrac{T_H}{T_C} - 1)$

above expression gives the expression of maximum amount of work.