Efficiency of an Engine

Efficiency is a measure of how effectively an engine converts heat energy into useful work. It is given by the ratio of the work output to the heat input. In this problem, we are given the information about two engines, A and B. We need to determine the efficiency of engine B.

1. Work Output Comparison:
- Engine A produces five times the work output compared to engine B per cycle.

2. Heat Input Comparison:
- Engine A receives three times the heat input compared to engine B.

3. Heat Exhaust Comparison:
- Engine A exhausts out twice the heat compared to engine B.

Efficiency Calculation:

To calculate the efficiency of an engine, we can use the following formula:

Efficiency = (Work Output / Heat Input) * 100

Let's denote the work output of engine B as Wb and the heat input as Qb.

According to the given information:
- Work output of engine A = 5 * Work output of engine B = 5Wb
- Heat input of engine A = 3 * Heat input of engine B = 3Qb
- Heat exhaust of engine A = 2 * Heat exhaust of engine B

The net heat supplied to the engine is equal to the heat input minus the heat exhaust. Therefore,
Heat supplied to engine B = Qb - (1/2) * Heat exhaust of engine B = Qb - (1/2) * (2 * Heat exhaust of engine B)
Heat supplied to engine B = Qb - Heat exhaust of engine B

Now, we can rewrite the efficiency formula for engine B:
Efficiency of engine B = (Work output of engine B / Heat supplied to engine B) * 100

Substituting the given values, we have:
Efficiency of engine B = (Wb / (Qb - Heat exhaust of engine B)) * 100

However, we need to express the heat exhaust of engine B in terms of Qb to simplify the equation.

Heat exhaust of engine A = 2 * Heat exhaust of engine B
Heat exhaust of engine B = (1/2) * Heat exhaust of engine A = (1/2) * 2 * Heat exhaust of engine B

Therefore, Heat exhaust of engine B = Heat exhaust of engine B

Simplifying the equation further:
Efficiency of engine B = (Wb / (Qb - Heat exhaust of engine B)) * 100
Efficiency of engine B = (Wb / (Qb - Heat exhaust of engine B)) * 100

Using the given information, we can substitute the values:
Efficiency of engine B = (Wb / (Qb - Heat exhaust of engine B)) * 100
Efficiency of engine B = (Wb / (Qb - (1/2) * 2 * Heat exhaust of engine B)) * 100
Efficiency of engine B = (Wb / (Qb - (1/2) * Heat exhaust of engine B)) * 100

Since the heat exhaust of engine B is equal to the heat exhaust of engine B, we can simplify the equation as follows:
Efficiency of engine B = (Wb / (Qb - (1/2) * Heat exhaust of engine B)) * 100

Given that the efficiency of engine B is 0.33 (or 33%), we