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. (%)

W=1,300 J

Q2=6,100 J
Q1 =?
W=Q1-Q2
Q1=W+Q2
efficiency =(Q1-Q2)/Q1 =W/Q1

To find the answers to these questions, we need to use the First Law of Thermodynamics, which states that the total energy of a system remains constant. In the case of a heat engine, the input energy (thermal energy) must equal the sum of the output energy (mechanical work) and the energy expelled.

Let's solve each part of the question step by step:

(a) To find the thermal energy added to the engine in each cycle, we add the mechanical work performed and the energy expelled by the engine. Mathematically, it can be represented as:
Thermal energy added = Mechanical work + Energy expelled

Thermal energy added = 1,300 J + 6,100 J
Thermal energy added = 7,400 J

Therefore, the thermal energy added to the engine in each cycle is 7,400 J.

(b) The thermal efficiency of a heat engine is defined as the ratio of the useful work output to the total energy input. Mathematically, it can be calculated as:
Thermal efficiency = (Useful work output / Total energy input) * 100

In this case, the useful work output is the mechanical work performed, and the total energy input is the thermal energy added to the engine.

Thermal efficiency = (1,300 J / 7,400 J) * 100
Thermal efficiency = 0.1757 * 100
Thermal efficiency ≈ 17.57%

Therefore, the thermal efficiency of the engine is approximately 17.57%.