Question

A Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. 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

Answer 1

Answer: (A)

0.417 kcal/s

Answer 2

The efficiency of the heat engine is
$\eta=1-\frac{T_{2}}{T_{1}}=1-\left(\frac{273+27 K}{273+427 K}\right)=\frac{4}{7}$
But $\eta=\frac{W}{\eta}=\frac{1.0 k W}{4/7}=1.75\, kW$
$=0.417\, Kcal/s$
Thus, the engine would require $417\, cal$ of heat per second, to deliver the requisite amount of work.