Answer:
A) 150%
B) 20.67 J
Explanation:
A) To determine the efficiency of the engine, we can use the formula:
efficiency = (work output / heat input) x 100%
In this case, the engine does 62 J of work each cycle, so the work output is 62 J. We're also given that the engine absorbs 2 times as much heat as it discharges to the environment, so we can express the heat input as 2 times the heat discharged:
heat input = 2 x heat discharged
Therefore, we can rewrite the efficiency formula as:
efficiency = (62 J / (2 x heat discharged)) x 100%
Simplifying this expression, we get:
efficiency = 31 J / heat discharged
Now we need to determine the value of heat discharged. We know that the engine absorbs 2 times as much heat as it discharges, so the net heat input is 3 times the heat discharged:
net heat input = heat input - heat discharged = 2 x heat discharged - heat discharged = heat discharged
Therefore, we can express the net heat input as:
net heat input = 3 x heat discharged
Now we can use the first law of thermodynamics, which states that the net heat input is equal to the work output plus the heat discharged:
net heat input = work output + heat discharged
Substituting the given values, we get:
3 x heat discharged = 62 J + heat discharged
Solving for heat discharged, we get:
heat discharged = 20.67 J
Now we can calculate the efficiency:
efficiency = 31 J / 20.67 J = 1.50 or 150%
Therefore, the efficiency of the engine is 150%.
B) To determine the quantity of heat discharged to the environment each cycle in Joules, we can use the value we calculated above for heat discharged:
heat discharged = 20.67 J
Therefore, the quantity of heat discharged to the environment each cycle is 20.67 J.
Hope this helps!