JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Heat & Thermodynamics

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Efficiency of a reversible heat engine will be highest at

- 27 3^{\circ} C

temperature of cold reservoir.
Reason R : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as

η = (1 - \frac{T _{2}}{T _{1}})

.
In the light of the above statements, choose the correct answer from the options given below :

(A) $A$ is true but $R$ is false
(B)Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$
(C) $A$ is false but $R$ is true
(D)Both $A$ and $R$ are true and $R$ is the correct explanation of A✓ Correct

Answer: (D)

Solution

The efficiency of a reversible Carnot engine is

η = 1 - \frac{T _{2}}{T _{1}}

, which depends on both the hot reservoir

T_{1}

and the cold reservoir

T_{2}

. For a fixed hot reservoir the efficiency rises as

T_{2}

falls, becoming greatest when

T_{2}

is lowest, namely

- 27 3^{\circ}

= 0

K, where

η \to 1

. The assertion is thus true, and the quoted relation is precisely the reason behind it, so both statements are true and the reason correctly explains the assertion.

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Heat & Thermodynamics

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