To solve this problem, we can use the Carnot efficiency formula and the first law of thermodynamics.
(a) The efficiency (η) of a Carnot engine is given by the formula:
η = 1 - (TL / TH)
where TL is the absolute temperature of the low-temperature reservoir and TH is the absolute temperature of the high-temperature reservoir.
Given: TL = 100 oC = 373 K (conversion from Celsius to Kelvin) TH = 850 oK
Using the formula, we can calculate the efficiency:
η = 1 - (373 K / 850 K) = 1 - 0.4388 ≈ 0.5612 or 56.12%
Therefore, the efficiency of the engine is approximately 56.12%.
(b) The amount of heat extracted from the high-temperature reservoir (QH) can be calculated using the work done by the engine per cycle (W) and the efficiency (η) of the engine. The formula is:
QH = W / η
Given: W = 1400 J (work done per cycle) η = 0.5612 (efficiency calculated above)
Using the formula, we can calculate the heat extracted from the high-temperature reservoir:
QH = 1400 J / 0.5612 ≈ 2494 J
Therefore, approximately 2494 J of heat is extracted from the high-temperature reservoir each cycle.