A heat engine exhausts 3 000 J of heat while performing 1 500 J of useful work. What is the efficiency of the engine?

Eff. = Output/Input = 1500/3000 = 0.50.

= 50%.

To find the efficiency of a heat engine, you can use the formula:

Efficiency = (Useful work output) / (Heat input)

In this case, the useful work output is given as 1,500 J, and the heat input (or heat exhausted) is given as 3,000 J. Plugging these values into the formula:

Efficiency = 1,500 J / 3,000 J = 0.5

Multiply by 100 to express the efficiency as a percentage:

Efficiency = 0.5 * 100 = 50%

Therefore, the efficiency of the engine is 50%.

To find the efficiency of the heat engine, we first need to understand the definition of efficiency. Efficiency is defined as the ratio of useful work output to the total input energy.

Given:
Heat exhausted by the engine (Qh) = 3,000 J
Useful work performed by the engine (W) = 1,500 J

The first step is to determine the total input energy, which in this case is the heat energy supplied to the engine (Qh). We can represent the total input energy as the sum of the useful work output (W) and the energy wasted or exhausted (Qc):

Total input energy (Qh) = Useful work output (W) + Wasted/Exhausted energy (Qc)

Rearranging the equation, we can solve for Qc:

Qc = Qh - W

Substituting the given values:

Qc = 3,000 J - 1,500 J
Qc = 1,500 J

Now, we can calculate the efficiency of the heat engine using the formula:

Efficiency = (Useful work output / Total input energy) * 100

Efficiency = (W / Qh) * 100

Substituting the given values:

Efficiency = (1,500 J / 3,000 J) * 100
Efficiency = 50%

Therefore, the efficiency of the heat engine is 50%.