Heat and Thermodynamics 5 Question 11
11. Three Carnot engines operate in series between a heat source at a temperature and a heat sink at temperature (see figure). There are two other reservoirs at temperatures and , as shown with . The three engines are equally efficient if
(Main 2019, 10 Jan I)
(a)
(b)
(c)
(d)
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Solution:
- Given, Carnot engines operates as,
As, efficiency of a Carnot’s engine is given by
We have,
For equal efficiencies,
Key idea In a Carnot engine the heat flow from higher temperature source
For the given condition, Carnot engine
where,
According to Carnot engine principle,
As per the given condition, if the work outputs of the two engines are equal, then