Question

A Carnot t engine operates between 227 degrees celsius it absorbs 6.0 * 10^4 cal cat Higher temperature the amount of heat converted into mechanical energy is equal to

Answer 1

Hello Dear.

Question is little bit incomplete. Correct Question will be →

A Carnot Engine operates between 227° C and 127°C. It absorbs 6 × 10⁴ Cal at higher temperature. The Amount of Heat Converted into Mechanical Energy is equal to ?

Now, Answer is Shown Below.

Work Input (or Heat Absorbs) = 6 × 10⁴ Cal.

T₁ = 127° C
 =(127 + 273) K. [Changing into kelvin]
 = 400 K.

T₂ = 227° C
 = (227 + 273) K. [Changing into kelvin]
 = 500 K.

∵ Efficiency = 1 - T₁/T₂
    = 1 - 400/500
    = (500 - 400)/500
   = 100/500
   = 1/5

Also, Efficiency = Work Output/Work Input

∴ 1/5 = Work Done/6 × 10⁴
∴ Work Done by the Carnot Engine = 60000/5
⇒ Work Done =  12000 Cal.


∴ Amount of Heat Converted into Mechanical Energy is 12000 Cal.

Note ⇒ The answer may be little bit different then the exact answer because I have taken the T₁ as 127 °C. It may be possible that in the book the value of Temperature is different. But the Methods of the Solution will be the same.So, you can change the Value of Temperature and apply the same method If the value in the question is different.


Hope it helps.

Answer 2

A Carnot Engine operates between 227° C and 127°C. It absorbs 6 × 10⁴ Cal at higher temperature. The Amount of Heat Converted into Mechanical Energy is equal to ?

Now, Answer is Shown Below.

Work Input (or Heat Absorbs) = 6 × 10⁴ Cal.

T₁ = 127° C

 =(127 + 273) K. [Changing into kelvin]

 = 400 K.

T₂ = 227° C

 = (227 + 273) K. [Changing into kelvin]

 = 500 K.

∵ Efficiency = 1 - T₁/T₂

   = 1 - 400/500

   = (500 - 400)/500

  = 100/500

  = 1/5

Also, Efficiency = Work Output/Work Input

∴ 1/5 = Work Done/6 × 10⁴

∴ Work Done by the Carnot Engine = 60000/5

⇒ Work Done =  12000 Cal.