Question

A scientist says that the efficiency of heat engine which work at source temperature 127°C
and sink temperature 27" C is 26 %, then ...
(A) it is imposible.
(B) it is possible but less probable.
(0) it is quite probable.
(D) data are incomplete.​

Answer 1

Answer:

Given:

Scientist claims that working temperature range of his machine is as follows :

Source Temperature = 127°

Sink temperature = 27°

To find:

If operation of such a machine is possible or not .

Conversion:

First convert all the temperature to Kelvin.

So, source temperature = 127 + 273 = 400 K

Sink temperature = 27 + 273 = 300 K

Formulas used:

Let efficiency be denoted by η

η = 1 - sink temp./source temp.

Calculation:

η = 1 - sink temp./source temp.

=> η = 1 - 300/400

=> η = 1 - ¾

=> η = ¼

=> η = 25%.

So maximum efficiency that can be obtained at the given temperature range is 25%.

So the scientist's claim was wrong.

Such an machine is not possible.

So option A) is correct.

Answer 2

Question :-

Given above ↑

Answer :-

→ (A) it is impossible

Explanation :-

Firstly change °c into Kelvin (k)

we have ,

$\to \: \sf t_1 = 127 \degree \: c \\ \\ \to \sf \: t_1 \: = 127 + 273 \: = 400 \: k \\ \bf and \\ \\ \to \: \sf t_2 = 27 \degree \: c = 27 + 273 = 300 \: k$

We know that ,

$\implies \: \sf \: efficiency \: ( \eta) = 1 - \frac{ t_2\: }{ \: t_1 \: } \: \\ \\ \implies \sf \eta = 1 - \frac{300}{400} \\ \\ \implies \sf \eta = \frac{400 - 300}{400} \\ \\ \implies \eta = \frac{100}{400} \\ \\ \implies \: \boxed{ \eta = \frac{1}{4} = 25 \: \%} \\ \\ \sf{hence \: 26\% \: efficiency \: is \: impossible}$

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Hope it will help you .