Engine 1 has an efficiency of 0.19 and requires 6000 J of input heat to perform a certain amount of work. Engine 2 has an efficiency of 0.23 and performs the same amount of work. How much input heat does the second engine require?
For Engine 1 :
1 = Q01 / Qi1 { eq.1 }
where, 1 = efficiency of first engine = 0.19
Q0 = output heat = ?
Qi = input heat for engine 1 = 6000 J
inserting all these values in above eq.
(0.19) = Q01 / (6000 J)
Q01 = 1140 J
For Engine 2 :
2 = Q02 / Qi2 { eq.2 }
where, 2 = efficiency of 2nd engine = 0.23
Q02 = Q01 = same amount of heat = 1140 J
Qi2 = input heat for engine 2 = ?
inserting all these values in eq.2,
(0.23) = (1140 J) / Qi2
Qi2 = (1140 J) / (0.23)
Qi2 = 4956.5 J
The second engine will require an input heat is 4956.5 J.
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