Abstract:
Thermodynamics of a heat engine running between two reservoirs of finite size and with well defined temperatures that is not in equilibrium. Importantly practical, heat engines that produce
useful work often operate between heat baths of limitless size and constant temperature. This study
examines the effectiveness of a heat engine that operates between two limited-size heat sources
with a temperature differential at startup. Due to the sources' finite heat capacity, the total amount
of work that can be produced by such a heat engine is restricted. First, look into how various
source parameters that affect heat capacity affect the heat engine's efficiency at maximum work
(EMW) in the quasi-static limit. Moreover, it is found that the efficiency of the engine operating in
finite time with maximum power of each cycle is achieved follows a simple universality as
η=𝜂/4+0(η2
C), where 𝜂is the Carnot efficiency determined by the initial temperature of the
sources. Within the linear response regime, it is discovered that there exists a power-efficiency
trade off depending on the ratio of heat capacities (γ) of the reservoirs for the engine; the uniform
temperature of the two reservoirs at final time τ is bounded from below by the entropy production
𝜎∝ 1/τ. Further obtain a universal efficiency at maximum power of the engine for arbitrary γ.
Our dings can be used to develop an optimization scenario for thermodynamic cycles with finite
sized reservoirs in practice., the figure of merit, a quantity defined as a product of scaled power
and scaled efficiency, is found to be greater than unity in range of 0 ≤ 𝜂 ≤ 1.025.
The figure of merit of model IV, ψ generally decreases from its peak value of 1.095 with an
increase in 𝜂 . Only in the medium 𝜂 0.4 values, the optimum working condition is preferred to
the maximum power working condition. Elsewhere, the maximum working condition is better than
the optimum working condition for the model. In model IV, the figure of merits, ψ, slightly
decreases from its value of about 1.095 to 1.01 as at 𝜂 increases from zero to 0.8.
