Multiple Choice
An aircraft engine takes in 9 kJ of heat and expels 6.4 kJ of heat each cycle. How much mechanical work does the engine do each cycle?
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
No, it violates the first law of thermodynamics.
B
No, it violates the second law of thermodynamics.
C
No, it violates both the first and second laws of thermodynamics.
D
Yes
Verified step by step guidance1
Understand the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted. In the context of a heat engine, this means the energy absorbed from the hot reservoir should equal the sum of the work done and the energy emitted to the cold reservoir.
Apply the first law of thermodynamics to the given problem: \( Q_{in} = W + Q_{out} \), where \( Q_{in} \) is the energy absorbed from the hot reservoir, \( W \) is the work done by the engine, and \( Q_{out} \) is the energy emitted to the cold reservoir.
Substitute the given values into the equation: \( 1200\, \text{J} = 500\, \text{J} + 700\, \text{J} \). Check if this equation holds true to verify compliance with the first law of thermodynamics.
Consider the second law of thermodynamics, which states that the efficiency of a heat engine is limited by the temperatures of the hot and cold reservoirs. The efficiency \( \eta \) is given by \( \eta = 1 - \frac{T_{cold}}{T_{hot}} \), where temperatures must be in Kelvin.
Convert the temperatures from Celsius to Kelvin: \( T_{hot} = 400 + 273 = 673\, \text{K} \) and \( T_{cold} = 80 + 273 = 353\, \text{K} \). Calculate the theoretical maximum efficiency and compare it to the actual efficiency \( \eta_{actual} = \frac{W}{Q_{in}} = \frac{500}{1200} \). Verify if the actual efficiency is less than or equal to the theoretical maximum efficiency.
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