- Home
- Standard 11
- Physics
11.Thermodynamics
normal
A heat engine has an efficiency of $\frac{1}{6}$. When the temeprature of sink is reduced by $62^{\circ} {C}$, its efficiency get doubled. The temeprature of the source is $.....^{\circ} {C}$
A
$37$
B
$99$
C
$62$
D
$124$
Solution
Using, $\eta=1-\frac{ T _2}{ T _1}$
or $\frac{T_2}{T_1}=1-\eta$
According to first case
$\frac{ T _2}{ T _1}=1-\frac{1}{6}=\frac{5}{6} \ldots .$. (i)
According to second case
$\frac{ T _2-62}{ T _1}=1-2 \times \frac{1}{6}=\frac{2}{3} \ldots \ldots$. (ii)
$\frac{ T _2}{ T _1}-\frac{62}{ T _1}=\frac{2}{3}$
From equations $(i)$ and $(ii)$, we get
$\frac{5}{6}-\frac{62}{ T _1}=\frac{2}{3} \Rightarrow \frac{5}{6}-\frac{2}{3}=\frac{62}{ T _1}$
$\Rightarrow \frac{1}{6}=\frac{62}{ T _1}$
$T _1=372 K \text { or } T _1=372-372$
$T _1=99^{\circ} C$
Standard 11
Physics
