Question

Consider a Carnot engine operating between temperatures of 600 K and 400 K. The engine performs 1000 J of work per cycle. The heat (in Joules) extracted per cycle from the high temperature reservoir is:

Hint:

For a Carnot engine, the efficiency depends on the temperatures of the hot and cold reservoirs, and the heat extracted from the hot reservoir can be calculated using the efficiency and the work done.

Answer 1

Step 1: Understanding the Carnot engine.
The efficiency of a Carnot engine is given by: \[ \eta = 1 - \frac{T_C}{T_H} \] where \( T_C = 400 \, \text{K} \) is the cold reservoir temperature and \( T_H = 600 \, \text{K} \) is the hot reservoir temperature. The work done per cycle \( W = 1000 \, \text{J} \). The heat extracted from the hot reservoir is \( Q_H \), and the efficiency is also given by: \[ \eta = \frac{W}{Q_H} \] Thus, we can solve for \( Q_H \): \[ Q_H = \frac{W}{1 - \frac{T_C}{T_H}} = \frac{1000}{1 - \frac{400}{600}} = \frac{1000}{\frac{1}{3}} = 3000 \, \text{J} \] Step 2: Conclusion.
Thus, the heat extracted per cycle from the high temperature reservoir is 3000 J.