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In a Carnot engine, efficiency is 40% at hot reservoir temperature T. For efficiency to be 50%, what shall be the temperature of the hot reservoir?
- a)T/5
- b)2T/5
- c)6T
- d)6T/5
Correct answer is option 'D'. Can you explain this answer?
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In a Carnot engine, efficiency is 40% at hot reservoir temperature T. ...
The efficiency of a heat engine is defined as the ratio of work done to the heat supplied, i.e.,
where T2 is temperature of sink,
and T1 is temperature of hot reservoir.
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In a Carnot engine, efficiency is 40% at hot reservoir temperature T. ...
Explanation:
Given:
Efficiency of the Carnot engine at hot reservoir temperature T = 40%
Formula:
Efficiency of a Carnot engine, E = 1 - (Tc/Th)
Where,
E = Efficiency
Tc = Temperature of the cold reservoir
Th = Temperature of the hot reservoir
Calculating the initial temperature of the hot reservoir:
Given, Efficiency (E) = 40%
Therefore, 0.4 = 1 - (Tc/T)
0.4 = 1 - (Th/T)
Th/T = 1 - 0.4
Th/T = 0.6
Th = 0.6T
Finding the new temperature for an efficiency of 50%:
To find the new temperature (Th') for an efficiency of 50%:
Efficiency (E') = 50% = 0.5
0.5 = 1 - (Tc/Th')
0.5 = 1 - (Th'/T)
Th'/T = 1 - 0.5
Th'/T = 0.5
Th' = 0.5T
Therefore, the temperature of the hot reservoir for an efficiency of 50% is 0.5T, which can also be represented as 6T/5. Hence, the correct answer is option 'D'.
Given:
Efficiency of the Carnot engine at hot reservoir temperature T = 40%
Formula:
Efficiency of a Carnot engine, E = 1 - (Tc/Th)
Where,
E = Efficiency
Tc = Temperature of the cold reservoir
Th = Temperature of the hot reservoir
Calculating the initial temperature of the hot reservoir:
Given, Efficiency (E) = 40%
Therefore, 0.4 = 1 - (Tc/T)
0.4 = 1 - (Th/T)
Th/T = 1 - 0.4
Th/T = 0.6
Th = 0.6T
Finding the new temperature for an efficiency of 50%:
To find the new temperature (Th') for an efficiency of 50%:
Efficiency (E') = 50% = 0.5
0.5 = 1 - (Tc/Th')
0.5 = 1 - (Th'/T)
Th'/T = 1 - 0.5
Th'/T = 0.5
Th' = 0.5T
Therefore, the temperature of the hot reservoir for an efficiency of 50% is 0.5T, which can also be represented as 6T/5. Hence, the correct answer is option 'D'.
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In a Carnot engine, efficiency is 40% at hot reservoir temperature T. For efficiency to be 50%, what shall be the temperature of the hot reservoir?a)T/5b)2T/5c)6Td)6T/5Correct answer is option 'D'. Can you explain this answer?
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