Question

A Carnot engine operating between temperatures T₁ and T₂ has efficiency 0.2. When T₂ is reduced by 50 K, its efficiency increases to 0.4. Then T₁ and T₂ are respectively ______.

Options

• 200 K, 150 K

• 250 K, 200 K

• 300 K, 250 K

• 300 K, 200 K

Answer 1

A Carnot engine operating between temperatures T₁ and T₂ has efficiency 0.2. When T₂ is reduced by 50 K, its efficiency increases to 0.4. Then T₁ and T₂ are respectively 250 K, 200 K.

Explanation:

When efficiency of carnot engine, η = 0.2 Efficiency of a Carnot engine,

η = `1-"T"_2/"T"_1` or 0.2 = `1-"T"_2/"T"_1` 

or `"T"_2/"T"_1` = 0.8                     ...(i)

When T₂ is reduced by 50 K, its efficiency becomes 0.4

∴ 0.4 = `1-("T"_2-50)/"T"_1`

or `("T"_2-50)/"T"_1` = 0.6           ...(ii)

Dividing eqn. (i) by (ii)

`"T"_2/("T"_2-50)=0.8/0.6=4/3`

⇒ 3T₂ = 4T₂ - 200 or T₂ = 200 K

From eqn. (ii), T₁ = `("T"_2-50)/0.6=(200-50)/0.6` = 250 K