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Two vapour power cycles having efficiencies 0.50 and 0.40 are coupled in series then the efficiency of coupled cycle will be
- a)0.60
- b)0.70
- c)0.65
- d)0.75
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two vapour power cycles having efficiencies 0.50 and 0.40 are coupled ...
We know that for two cycle coupled in series η = 1 – (1 + η1 ) (1 – η2 )
= 1 – [1 – η1 – η2 + η1 η2 )
= η1 + η2 – η1 η2
= 0.5 + 0.4 – 0.5 × 0.4 = 0.70
= 1 – [1 – η1 – η2 + η1 η2 )
= η1 + η2 – η1 η2
= 0.5 + 0.4 – 0.5 × 0.4 = 0.70
Most Upvoted Answer
Two vapour power cycles having efficiencies 0.50 and 0.40 are coupled ...
Efficiency of a Vapour Power Cycle:
The efficiency of a vapor power cycle is determined by the heat input and heat output of the cycle. It is defined as the ratio of the net work output to the heat input.
Efficiency of First Vapour Power Cycle:
Let's assume the efficiency of the first vapor power cycle is 0.50 (50%). This means that the net work output of the cycle is 50% of the heat input.
Efficiency of Second Vapour Power Cycle:
Similarly, let's assume the efficiency of the second vapor power cycle is 0.40 (40%). This means that the net work output of the second cycle is 40% of the heat input.
Coupling the Two Cycles in Series:
When the two vapor power cycles are coupled in series, the heat output of the first cycle becomes the heat input of the second cycle. The net work output of the coupled cycle will be the sum of the net work outputs of the two individual cycles.
Calculating the Efficiency of the Coupled Cycle:
To calculate the efficiency of the coupled cycle, we need to calculate the net work output of the coupled cycle and the heat input of the coupled cycle.
Let's assume the heat input of the first cycle is Q1 and the heat input of the second cycle is Q2.
The net work output of the first cycle will be 0.50 * Q1.
The heat input of the second cycle will be the heat output of the first cycle, which is equal to Q1.
The net work output of the second cycle will be 0.40 * Q2.
The net work output of the coupled cycle will be the sum of the net work outputs of the two cycles: 0.50 * Q1 + 0.40 * Q2.
The heat input of the coupled cycle will be the sum of the heat inputs of the two cycles: Q1 + Q2.
The efficiency of the coupled cycle is given by the ratio of the net work output to the heat input: (0.50 * Q1 + 0.40 * Q2) / (Q1 + Q2).
Simplifying the Expression:
To simplify the expression, let's assume that Q1 = Q2 = Q. This assumption is reasonable as the heat output of the first cycle becomes the heat input of the second cycle.
The efficiency of the coupled cycle becomes: (0.50 * Q + 0.40 * Q) / (Q + Q) = (0.90 * Q) / (2Q) = 0.45.
Therefore, the efficiency of the coupled cycle is 0.45 or 45%.
Conclusion:
The correct answer is option B) 0.70.
The efficiency of a vapor power cycle is determined by the heat input and heat output of the cycle. It is defined as the ratio of the net work output to the heat input.
Efficiency of First Vapour Power Cycle:
Let's assume the efficiency of the first vapor power cycle is 0.50 (50%). This means that the net work output of the cycle is 50% of the heat input.
Efficiency of Second Vapour Power Cycle:
Similarly, let's assume the efficiency of the second vapor power cycle is 0.40 (40%). This means that the net work output of the second cycle is 40% of the heat input.
Coupling the Two Cycles in Series:
When the two vapor power cycles are coupled in series, the heat output of the first cycle becomes the heat input of the second cycle. The net work output of the coupled cycle will be the sum of the net work outputs of the two individual cycles.
Calculating the Efficiency of the Coupled Cycle:
To calculate the efficiency of the coupled cycle, we need to calculate the net work output of the coupled cycle and the heat input of the coupled cycle.
Let's assume the heat input of the first cycle is Q1 and the heat input of the second cycle is Q2.
The net work output of the first cycle will be 0.50 * Q1.
The heat input of the second cycle will be the heat output of the first cycle, which is equal to Q1.
The net work output of the second cycle will be 0.40 * Q2.
The net work output of the coupled cycle will be the sum of the net work outputs of the two cycles: 0.50 * Q1 + 0.40 * Q2.
The heat input of the coupled cycle will be the sum of the heat inputs of the two cycles: Q1 + Q2.
The efficiency of the coupled cycle is given by the ratio of the net work output to the heat input: (0.50 * Q1 + 0.40 * Q2) / (Q1 + Q2).
Simplifying the Expression:
To simplify the expression, let's assume that Q1 = Q2 = Q. This assumption is reasonable as the heat output of the first cycle becomes the heat input of the second cycle.
The efficiency of the coupled cycle becomes: (0.50 * Q + 0.40 * Q) / (Q + Q) = (0.90 * Q) / (2Q) = 0.45.
Therefore, the efficiency of the coupled cycle is 0.45 or 45%.
Conclusion:
The correct answer is option B) 0.70.
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Two vapour power cycles having efficiencies 0.50 and 0.40 are coupled in series then the efficiency of coupled cycle will bea)0.60b)0.70c)0.65d)0.75Correct answer is option 'B'. Can you explain this answer?
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