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Two reversible engines are connected in series between a heat source and a sink. The efficiencies of these engines are 60% and 50%, respectively. If these two engines are replaced by a single reversible engine, the efficiency of this engine will be
- a)60%
- b)70%
- c)80%
- d)90%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two reversible engines are connected in series between a heat source a...
Let we supply 1 kJ of hat to engine 1 and the rejected heat of engine 1 will go to engine 2.
Now, if both engines are replaced by a single engine. So,
∴Efficiencyofnewengine=1−0.21=0.8=80%∴Efficiencyofnewengine=1−0.21=0.8=80%
Short trick: -
ηoverall = η1 + η2 - η1η2
= 0.6 + 0.5 - 0.6 × 0.5 = 0.8 = 80%
Most Upvoted Answer
Two reversible engines are connected in series between a heat source a...
Efficiency of a heat engine is defined as the ratio of the work output to the heat input. In other words, it is the percentage of energy input that is converted into useful work.
When two reversible engines are connected in series, the output of the first engine becomes the input for the second engine. The overall efficiency of the system is determined by the product of the efficiencies of the individual engines.
Let's assume the heat input to the system is Q.
Efficiency of the first engine = 60% = 0.6
Therefore, the work output of the first engine = 0.6Q
The heat output from the first engine becomes the heat input for the second engine.
Heat input to the second engine = 0.6Q
Efficiency of the second engine = 50% = 0.5
Therefore, the work output of the second engine = 0.5 * 0.6Q = 0.3Q
The total work output of the system is the sum of the work outputs of the individual engines.
Total work output = Work output of the first engine + Work output of the second engine
= 0.6Q + 0.3Q
= 0.9Q
The efficiency of the overall system is given by the ratio of the total work output to the heat input.
Efficiency of the overall system = Total work output / Heat input
= 0.9Q / Q
= 0.9
Therefore, the efficiency of the single reversible engine that replaces the two engines in series is 90% or 0.9, which corresponds to option 'C'.
When two reversible engines are connected in series, the output of the first engine becomes the input for the second engine. The overall efficiency of the system is determined by the product of the efficiencies of the individual engines.
Let's assume the heat input to the system is Q.
Efficiency of the first engine = 60% = 0.6
Therefore, the work output of the first engine = 0.6Q
The heat output from the first engine becomes the heat input for the second engine.
Heat input to the second engine = 0.6Q
Efficiency of the second engine = 50% = 0.5
Therefore, the work output of the second engine = 0.5 * 0.6Q = 0.3Q
The total work output of the system is the sum of the work outputs of the individual engines.
Total work output = Work output of the first engine + Work output of the second engine
= 0.6Q + 0.3Q
= 0.9Q
The efficiency of the overall system is given by the ratio of the total work output to the heat input.
Efficiency of the overall system = Total work output / Heat input
= 0.9Q / Q
= 0.9
Therefore, the efficiency of the single reversible engine that replaces the two engines in series is 90% or 0.9, which corresponds to option 'C'.
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Suppose engines are parallel then efficiency will be..?
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Two reversible engines are connected in series between a heat source and a sink. The efficiencies of these engines are 60% and 50%, respectively. If these two engines are replaced by a single reversible engine, the efficiency of this engine will bea)60%b)70%c)80%d)90%Correct answer is option 'C'. Can you explain this answer?
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