Q4. A Carnot engine has an efficiency of 40% with its source at 600 K. Find the sink temperature in °C.
T2 = T1(1 − η) = 600 × 0.6 = 360 K, approximately 87 °C.
Q5. A Carnot engine takes in 2000 J of heat from a source at 400 K and rejects heat to a sink at 300 K. Find the heat rejected and the work done.
Q2 = 2000 × 300/400 = 1500 J. W = 2000 − 1500 = 500 J (efficiency 25%).
Q6. Why does the efficiency of a Carnot engine not depend on whether the working substance is an ideal gas, steam or anything else?
If one reversible engine between the same two temperatures were more efficient than another, running the less efficient one backwards as a refrigerator alongside it would turn heat from one reservoir completely into work, breaking the second law. So all reversible engines between the same two temperatures have the same efficiency, 1 − T2/T1.