In each cycle of its operation, a heat engine expels 6,100 J of energy and performs 1,300 J of mechanical work.
(a) How much thermal energy must be added to the engine in each cycle?_____J
(b) Find the thermal efficiency of the engine.____%
a
6100 + 1300 = 7,400 J
b
work out/heat in = 13/74 = .176 = 17.6 %
(a) To find the amount of thermal energy added to the engine in each cycle, we need to apply the first law of thermodynamics. According to the first law, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the internal energy change is zero since the engine is in a cycle.
So, we have:
ΔU = Q - W
Since ΔU is zero, we can rewrite the equation as:
0 = Q - W
Now, we can substitute the given values:
Q - 6100 J = 0
To find Q, we can rearrange the equation:
Q = 6100 J
Therefore, the amount of thermal energy added to the engine in each cycle is 6100 J.
(b) The thermal efficiency of an engine is defined as the ratio of the work done by the engine to the thermal energy added to the engine. Mathematically, it can be expressed as:
Efficiency = (Work done / Thermal energy added) × 100
Given that the work done by the engine is 1300 J and the thermal energy added is 6100 J, we can substitute these values into the efficiency formula:
Efficiency = (1300 J / 6100 J) × 100
Efficiency ≈ 0.2131 × 100
Therefore, the thermal efficiency of the engine is approximately 21.31%.