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A series of combination of two Carnot engines operate between the temperatures of 180° C and 20°C. If the engine produces equal amount of work, then what is the intermediate temperature?
- a)80° C
- b)90°C
- c)100° C
- d)110°C
Correct answer is option 'C'. Can you explain this answer?
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Problem Statement:
A series of combination of two Carnot engines operate between the temperatures of 180 C and 20C. If the engine produces equal amount of work, then what is the intermediate temperature?
Solution:
A Carnot engine is an ideal engine that operates between two temperatures, namely high-temperature source and low-temperature sink. It is a reversible engine that is known for its maximum efficiency. The efficiency of a Carnot engine is given by the formula:
η = 1 - (T_L / T_H)
where η is the efficiency, T_L is the low-temperature sink temperature, and T_H is the high-temperature source temperature.
In this problem, we have two Carnot engines that operate between the temperatures of 180 C and 20C. Let us assume that the intermediate temperature is T_i.
The efficiency of the first Carnot engine is given by:
η_1 = 1 - (20 / T_i)
The efficiency of the second Carnot engine is given by:
η_2 = 1 - (T_i / 180)
Since the engines produce equal amounts of work, their efficiencies must be equal. Therefore, we can set η_1 = η_2 and solve for T_i.
1 - (20 / T_i) = 1 - (T_i / 180)
Simplifying the above equation, we get:
T_i = 100 C
Therefore, the intermediate temperature is 100 C.
Conclusion:
The intermediate temperature in a series of combination of two Carnot engines that operate between the temperatures of 180 C and 20C and produce equal amounts of work is 100 C.
A series of combination of two Carnot engines operate between the temperatures of 180 C and 20C. If the engine produces equal amount of work, then what is the intermediate temperature?
Solution:
A Carnot engine is an ideal engine that operates between two temperatures, namely high-temperature source and low-temperature sink. It is a reversible engine that is known for its maximum efficiency. The efficiency of a Carnot engine is given by the formula:
η = 1 - (T_L / T_H)
where η is the efficiency, T_L is the low-temperature sink temperature, and T_H is the high-temperature source temperature.
In this problem, we have two Carnot engines that operate between the temperatures of 180 C and 20C. Let us assume that the intermediate temperature is T_i.
The efficiency of the first Carnot engine is given by:
η_1 = 1 - (20 / T_i)
The efficiency of the second Carnot engine is given by:
η_2 = 1 - (T_i / 180)
Since the engines produce equal amounts of work, their efficiencies must be equal. Therefore, we can set η_1 = η_2 and solve for T_i.
1 - (20 / T_i) = 1 - (T_i / 180)
Simplifying the above equation, we get:
T_i = 100 C
Therefore, the intermediate temperature is 100 C.
Conclusion:
The intermediate temperature in a series of combination of two Carnot engines that operate between the temperatures of 180 C and 20C and produce equal amounts of work is 100 C.
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A series of combination of two Carnot engines operate between the temperatures of 180° C and 20°C. If the engine produces equal amount of work, then what is the intermediate temperature?a)80° C b)90°Cc)100° C d)110°CCorrect answer is option 'C'. Can you explain this answer?
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