A Carnot engine has efficiency of 50 %. If the temperature of sink is reduced by 40° C, its efficiency increases by 30 %. The temperature of the source will be :

Question

A Carnot engine has efficiency of 50 %. If the temperature of sink is reduced by 40° C, its efficiency increases by 30 %. The temperature of the source will be : (A) 166.7 K (B) 255.1 K (C) 266.7 K (D) 367.7 K

Tardigrade Admin · Accepted Answer

η=1-( T L / T H ) (1/2)=1-( T L / T H ) (1/2)(1 ⋅ 3)=1-(( T L -40/ T H )) (1/2)(1 ⋅ 3)=(1/2)+(40/ T H ) T H =266.7 K

Q. A Carnot engine has efficiency of $50%$ . If the temperature of sink is reduced by $4 0^{\circ} C$ , its efficiency increases by $30%$ . The temperature of the source will be :

$166.7 K$

$255.1 K$

$266.7 K$

$367.7 K$

$η = 1 - \frac{T _{L}}{T _{H}}$
$\frac{1}{2} = 1 - \frac{T _{L}}{T _{H}}$
$\frac{1}{2} (1 \cdot 3) = 1 - (\frac{T _{L} - 40}{T _{H}})$
$\frac{1}{2} (1 \cdot 3) = \frac{1}{2} + \frac{40}{T _{H}}$
$T_{H} = 266.7 K$

Q. A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40∘C, its efficiency increases by 30%. The temperature of the source will be :

166.7K

255.1K

266.7K

367.7K