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A Carnot engine whose efficiency is 50% has an exhaust temperature of 500 K. If the efficiency is to be 60% with the same intake temperature, the exhaust temperature must be (in K) [2002]
- a)800
- b)200
- c)400
- d)600
Correct answer is option 'C'. Can you explain this answer?
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A Carnot engine whose efficiency is 50% has an exhaust temperature of ...
⇒ T1 = 1000K
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A Carnot engine whose efficiency is 50% has an exhaust temperature of ...
Given:
Efficiency of the Carnot engine = 50%
Exhaust temperature = 500 K
To find:
Exhaust temperature for an efficiency of 60%
Formula:
Efficiency of a Carnot engine = 1 - (T2/T1)
where T2 is the exhaust temperature and T1 is the intake temperature.
Calculation:
Let's assume the intake temperature is T1.
Given that the efficiency of the Carnot engine is 50%, we can write:
0.5 = 1 - (500/T1)
(500/T1) = 1 - 0.5
(500/T1) = 0.5
T1 = 1000 K
Now, we need to find the exhaust temperature for an efficiency of 60%.
Using the same formula, we have:
0.6 = 1 - (T2/1000)
(T2/1000) = 1 - 0.6
(T2/1000) = 0.4
T2 = 0.4 * 1000
T2 = 400 K
Therefore, the exhaust temperature for an efficiency of 60% is 400 K. Hence, option C is the correct answer.
Efficiency of the Carnot engine = 50%
Exhaust temperature = 500 K
To find:
Exhaust temperature for an efficiency of 60%
Formula:
Efficiency of a Carnot engine = 1 - (T2/T1)
where T2 is the exhaust temperature and T1 is the intake temperature.
Calculation:
Let's assume the intake temperature is T1.
Given that the efficiency of the Carnot engine is 50%, we can write:
0.5 = 1 - (500/T1)
(500/T1) = 1 - 0.5
(500/T1) = 0.5
T1 = 1000 K
Now, we need to find the exhaust temperature for an efficiency of 60%.
Using the same formula, we have:
0.6 = 1 - (T2/1000)
(T2/1000) = 1 - 0.6
(T2/1000) = 0.4
T2 = 0.4 * 1000
T2 = 400 K
Therefore, the exhaust temperature for an efficiency of 60% is 400 K. Hence, option C is the correct answer.
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A Carnot engine whose efficiency is 50% has an exhaust temperature of 500 K. If the efficiency is to be 60% with the same intake temperature, the exhaust temperature must be (in K) [2002]a)800b)200c)400d)600Correct answer is option 'C'. Can you explain this answer?
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