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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$. When the temperature of cold reservoir raised by $x$, its efficiency decreases to $\frac{1}{6}$. The value of $x$, if the temperature of hot reservoir is $99^{\circ}\,C$, will be $........\,K$
  • A
    $16.5$
  • B
    $33$
  • C
    $66$
  • ✓
    $62$
✓

Answer

Correct option: D.
$62$
d
$T _{ H }=99^{\circ} C =99+273$

$\qquad=372\,K$

$1-\frac{ T _{ C }}{ T _{ H }}=\frac{1}{3}$

$\frac{ T _{ C }}{ T _{ H }}=\frac{2}{3} \quad(1) \Rightarrow T _{ C }=\frac{2}{3} \times 372$

$1-\frac{ T _{ C }+ X }{ T _{ H }}=\frac{1}{6}$

$\frac{5}{6}=\frac{ T _{ C }+ X }{ T _{ H }}$

$\frac{5}{6}=\frac{248+ X }{372}$

$248+ X =5 \times 62$

$X =310-248=62\,K$

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