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Out of three Carnot engines, operating between reservoir temperature of (a) 400 and 500 K (b) 600 and 800 K (c) 400 and 600 K, which has the greater thermal efficiency?
- a)a
- b)b
- c)c
- d)All the above have same efficiency
Correct answer is option 'C'. Can you explain this answer?
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Out of three Carnot engines, operating between reservoir temperature o...
Introduction:
Carnot engines are idealized heat engines that operate on the reversible Carnot cycle. The efficiency of a Carnot engine is determined by the temperature difference between the hot and cold reservoirs. In this case, we have three Carnot engines operating between different temperature ranges, and we need to determine which engine has the greater thermal efficiency.
Explanation:
To compare the thermal efficiencies of the three Carnot engines, we need to calculate the efficiency for each engine using the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Engine (a):
Temperature range: 400 K to 500 K
Efficiency = 1 - (400/500) = 1 - 0.8 = 0.2
Engine (b):
Temperature range: 600 K to 800 K
Efficiency = 1 - (600/800) = 1 - 0.75 = 0.25
Engine (c):
Temperature range: 400 K to 600 K
Efficiency = 1 - (400/600) = 1 - 0.67 = 0.33
Comparison:
From the calculations, we can see that Engine (c) has the highest thermal efficiency of 0.33, followed by Engine (b) with an efficiency of 0.25, and Engine (a) with the lowest efficiency of 0.2. Therefore, the correct answer is option 'C', Engine (c) has the greater thermal efficiency.
Conclusion:
The thermal efficiency of a Carnot engine is determined by the temperature difference between the hot and cold reservoirs. In this case, Engine (c) operating between a temperature range of 400 K to 600 K has the highest efficiency compared to Engine (a) and Engine (b). The efficiency of Engine (c) is 0.33, while the efficiencies of Engine (a) and Engine (b) are 0.2 and 0.25 respectively.
Carnot engines are idealized heat engines that operate on the reversible Carnot cycle. The efficiency of a Carnot engine is determined by the temperature difference between the hot and cold reservoirs. In this case, we have three Carnot engines operating between different temperature ranges, and we need to determine which engine has the greater thermal efficiency.
Explanation:
To compare the thermal efficiencies of the three Carnot engines, we need to calculate the efficiency for each engine using the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Engine (a):
Temperature range: 400 K to 500 K
Efficiency = 1 - (400/500) = 1 - 0.8 = 0.2
Engine (b):
Temperature range: 600 K to 800 K
Efficiency = 1 - (600/800) = 1 - 0.75 = 0.25
Engine (c):
Temperature range: 400 K to 600 K
Efficiency = 1 - (400/600) = 1 - 0.67 = 0.33
Comparison:
From the calculations, we can see that Engine (c) has the highest thermal efficiency of 0.33, followed by Engine (b) with an efficiency of 0.25, and Engine (a) with the lowest efficiency of 0.2. Therefore, the correct answer is option 'C', Engine (c) has the greater thermal efficiency.
Conclusion:
The thermal efficiency of a Carnot engine is determined by the temperature difference between the hot and cold reservoirs. In this case, Engine (c) operating between a temperature range of 400 K to 600 K has the highest efficiency compared to Engine (a) and Engine (b). The efficiency of Engine (c) is 0.33, while the efficiencies of Engine (a) and Engine (b) are 0.2 and 0.25 respectively.
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Community Answer
Out of three Carnot engines, operating between reservoir temperature o...
Efficiency= difference of temp of reservoirs/ the temperature of source
thus
eta 1= 100/500=0.2
eta 2=200/800=0.25
eta 3=200/600=0.33
thus (c) has greatest thermal efficiency
thus
eta 1= 100/500=0.2
eta 2=200/800=0.25
eta 3=200/600=0.33
thus (c) has greatest thermal efficiency
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