Consider an inefficient engine which draws 200 J of heat from a hot reservoir at 100oC, converts 48 J to work, and rejects 152 J to a cold reservoir at 0oC. Theoretically, how much maximum work can be produced if the efficiency of the engine is maximized? How much work was “lost” by using this inefficient heat engine design? (Hint: Carnot Engine)

How did you get that?

Duplicate post. See my answer posted later. 444 is wrong, by the way.

To determine the maximum work that can be produced and the work lost by using this inefficient heat engine design, we can use the Carnot engine as a reference point.

The Carnot engine is the most efficient heat engine possible, operating between two temperature reservoirs. According to the Carnot efficiency formula, the efficiency of a heat engine can be calculated as:

η = 1 - (Tc/Th)

Where η is the efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

In this case, the hot reservoir is at 100°C (or 373 Kelvin) and the cold reservoir is at 0°C (or 273 Kelvin).

Using the Carnot efficiency formula, we can calculate the maximum theoretical efficiency of the engine as:

η_carnot = 1 - (273/373) = 0.2679 or 26.79%

Now, let's calculate the maximum work that can be produced by this heat engine. The maximum work can be calculated using the formula:

W_max = η_carnot * Qh

Where W_max is the maximum work, η_carnot is the Carnot efficiency, and Qh is the heat energy provided by the hot reservoir.

In this case, Qh is given as 200 J. Substituting the values, we have:

W_max = 0.2679 * 200 = 53.58 J

Therefore, the maximum work that can be produced when the efficiency is maximized is 53.58 J.

To determine the work lost by using this inefficient heat engine design, we can subtract the work produced by this engine from the maximum work:

Work_lost = W_max - 48

Substituting the values, we have:

Work_lost = 53.58 - 48 = 5.58 J

Therefore, the work lost by using this inefficient heat engine design is 5.58 J.

In summary, the maximum work that can be produced when the efficiency is maximized is 53.58 J, while 5.58 J of work is lost by using this inefficient heat engine design.