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 ______.

Options

• 166.7 K

• 255.1 K

• 266.7 K

• 367.7 K

Answer 1

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 266.7 K.

Explanation:

Efficiency, `eta = 1 - T_L/T_H`

Given η = 50%

∴ `1/2 = 1 - T_L/T_H`

when η increases 30% then,

`1/2(1.3) = 1 - ((T_L - 40)/T_H)`

⇒ `1/2(1.3) = 1/2 + 40/T_H`

∴ T_H = 266.7 K