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Answer :
Final answer:
The maximum efficiency of a steam engine exhausting at 270°C using 450°C steam is 24.9%. A second engine using the exhaust from the first engine, exhausting at 150°C, would have a maximum efficiency of 22.1%.
Explanation:
To find the maximum efficiency of a heat engine, we can use the Carnot efficiency formula, which is given by 1 - (Tc/Th), where Tc and Th are the absolute temperatures of the cold and hot reservoirs respectively. It is important to convert temperatures from Celsius to Kelvin by adding 273.15.
(a) First Engine Efficiency:
- Th = 450 °C + 273.15 = 723.15 K
- Tc = 270 °C + 273.15 = 543.15 K
- Maximum efficiency = 1 - (543.15 / 723.15) = 0.249 or 24.9%
(b) Second Engine Efficiency:
- New Th (from the first engine's exhaust) = 270 °C + 273.15 = 543.15 K
- New Tc = 150 °C + 273.15 = 423.15 K
- Maximum efficiency = 1 - (423.15 / 543.15) = 0.221 or 22.1%
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