Multiple Choice
A heat engine uses a tank of ice water as a cold reservoir. The engine takes in 8 kJ of heat from the hot reservoir, and the heat expelled melts 18g of ice in the tank. How much work does this engine do?
23. The Second Law of Thermodynamics
Heat Engines and the Second Law of Thermodynamics
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In each cycle, a heat engine absorbs from a 400°C hot reservoir, emits to 80°C cold reservoir, while doing of work. Is it physically possible for this engine to exist?
A
Yes
B
No, it violates the first law of thermodynamics.
C
No, it violates both the first and second laws of thermodynamics.
D
No, it violates the second law of thermodynamics.
Verified step by step guidance1
Understand the second law of thermodynamics, which states that the total entropy of a system and its surroundings always increases for any real process. This implies that no heat engine can be 100% efficient.
Calculate the efficiency of the heat engine using the formula:
where is the work done and is the heat absorbed from the hot reservoir.
Substitute the given values into the efficiency formula:
which simplifies to 0.5 or 50%.
Calculate the Carnot efficiency, which is the maximum possible efficiency for a heat engine operating between two temperatures. Use the formula:
where and are the absolute temperatures of the cold and hot reservoirs respectively.
Convert the temperatures from Celsius to Kelvin and substitute them into the Carnot efficiency formula:
which results in a Carnot efficiency less than 50%. Since the actual efficiency exceeds the Carnot efficiency, the engine violates the second law of thermodynamics.
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