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. 1.3 kcal/s
• C. 18.1 kcal/s
• D. 0.212 kcal/s

Hint:

The efficiency of a Carnot engine depends on the temperatures of the hot and cold reservoirs. The heat consumed is related to the work done by the efficiency.

Answer 1

The Correct Option is A

Step 1: Apply the Carnot engine formula.
The efficiency of a Carnot engine is \( \eta = 1 - \frac{T_2}{T_1} \), where \( T_1 = 427 + 273 = 700 \, \text{K} \) and \( T_2 = 27 + 273 = 300 \, \text{K} \).
Step 2: Calculate the heat consumed.
The mechanical work delivered is 1.0 kW, and using the relation \( W = \eta Q \), we find the heat consumed per second to be 0.417 kcal/s. Final Answer: \[ \boxed{0.417 \, \text{kcal/s}} \]