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  • In case, Carnot engine operates between temperatures <img alt="300 \mathrm{~K}$ a

In 1^{\text {st }} case, Carnot engine operates between temperatures 300 \mathrm{~K}$ and $100 \mathrm{~K}. In 2^{\text {nd }} case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2^{\text {nd }} case) will be :

Option: 1

Same as the \mathrm{1^{st}} case


Option: 2

always greater then the \mathrm{1^{st}} case.


Option: 3

always less than the 1\mathrm{^{st}} case.


Option: 4

may increase or decrease with respact to the 1\mathrm{^{st}} case.


Answers (1)

best_answer

Case 1

\mathrm{\eta _{1}=1-\frac{T_{1}}{T_{2}}=1-\frac{100}{300}}

\mathrm{\eta _{1}=\frac{2}{3}\rightarrow (1)}

Case 2

The efficiency of the combination

\mathrm{\eta _{2}=\eta ^{'}.\eta ^{"}}

      \mathrm{=\left ( 1-\frac{200}{300} \right )\left ( 1-\frac{100}{200} \right )}

\mathrm{\eta _{2}=\frac{1}{3}\times \frac{1}{2}=\frac{1}{6}}

The efficiency in the 2nd case is less than the 1st case

Hence 3 is correct option

Posted by

Irshad Anwar

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