A Carnot's heat engine works between the temperatures 427° C and 27° C. What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0 kW ?

Question

A Carnot's heat engine works between the temperatures 427° C and 27° C. What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0 kW ? (A) 0.417 kcal/s (B) 4.17 kcal /s (C) 41.7 kcal/s (D) 0.212 kcal/s

Tardigrade Admin · Accepted Answer

The efficiency of the heat engine is η=1-(T2/T1)=1-((273+27 K/273+427 K))=(4/7) But η=(W/η)=(1.0 k W/4/7)=1.75 kW =0.417 Kcal/s Thus, the engine would require 417 cal of heat per second, to deliver the requisite amount of work.

Q. A Carnot's heat engine works between the temperatures 427∘C and 27∘C. What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0kW ?

0.417 kcal/s

4.17 kcal /s

41.7 kcal/s

0.212 kcal/s

The efficiency of the heat engine is η=1−T1​T2​​=1−(273+427K273+27K​)=74​ But η=ηW​=4/71.0kW​=1.75kW =0.417Kcal/s Thus, the engine would require 417cal of heat per second, to deliver the requisite amount of work.

Q. A Carnot's heat engine works between the temperatures $42 7^{\circ} C$ and $2 7^{\circ} C$ . What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 kW$ ?