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JEE Main 202125 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Evening Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2021 · 25 July · Evening Shift · Physics · Thermodynamics

A heat engine has an efficiency of (1)/(6) . When the temperature...

A heat engine has an efficiency of 16\dfrac{1}{6}. When the temperature of sink is reduced by 62°C62 ° C, its efficiency get doubled. The temperature of the source is :

Options

  1. A124°C124 ° C
  2. B37°C37 ° C
  3. C62°C62 ° C
  4. D99°C99 ° C

Correct answer

D. 99°C99 ° C

Step-by-step solution

η=1−TLTHη = 1 - \dfrac{{T}_{L}}{{T}_{H}} ......(i)

2η=1−(TL−62)TH=1−TLTH+62TH2η = 1 - \dfrac{\left({T}_{L} - 62\right)}{{T}_{H}} = 1 - \dfrac{{T}_{L}}{{T}_{H}} + \dfrac{62}{{T}_{H}}

⇒η=62TH⇒16=62TH⇒TH=6×62=372K⇒ η = \dfrac{62}{{T}_{H}} ⇒ \dfrac{1}{6} = \dfrac{62}{{T}_{H}} ⇒ {T}_{H} = 6 \times 62 = 372K

In C∘⇒372−273=99°CC ∘ ⇒ 372 - 273 = 99 ° C

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