Question

Let η₁ is the efficiency of an engine at T₁ = 447°C and T₂ = 147°C while η₂, is the efficiency at T₁ = 947°C and T₂ = 47°C. The ratio `eta_1/eta_2` will be ______.

Options

• 0.41

• 0.56

• 0.73

• 0.70

Answer 1

Let η₁ is the efficiency of an engine at T₁ = 447°C and T₂ = 147°C while η₂, is the efficiency at T₁ = 947°C and T₂ = 47°C. The ratio `eta_1/eta_2` will be 0.56.

Explanation:

Efficiency of heat engine is given as η = `1-"T"_"L"/"T"_"H"`

For T₁ = 447°C and T₂ = 147°C

η₁ = `1-(147+273)/(447+273)=1-420/720`

⇒ η₁ = `300/200`

For T₁ =  947°C and T₂ = 47°C

η₂ = `1-(47+273)/(947+273)=1-320/1220`

⇒ η₂ = `900/1220`

so, `eta_1/eta_2=300/720xx1220/900`

= `122/(72xx3)`

⇒ `eta_1/eta_2` = 0.56