The hot reservoir for a Carnot engine has a temperature of 926 K, while the cold reservoir has a temperature of 441 K. The heat input for this engine is 3730 J. The 441-K reservoir also serves as the hot reservoir for a second Carnot engine. This second engine uses the rejected heat of the first engine as input and extracts additional work from it. The rejected heat from the second engine goes into a reservoir that has a temperature of 191 K. Find the total work delivered by the two engines.

The efficiency of the first Carnot engine is

1 - (441/926) = 0.5238
The work out of that engine is 3730*0.5238 = 1954 J
The heat output of that engine is 3730-1954 = 1776 J. That heat is the input to the second engine. The second engine's efficiency is
1 - (191/441) = 0.5669. Its work output is
1776*0.5669 = 1007 J
Add the work outputs of the two engines for the final answer.

To find the total work delivered by the two engines, we need to calculate the work output of each engine separately and then add them together.

The work output of a Carnot engine is given by the formula:

W = Qh * (1 - Tc/Th)

Where W is the work output, Qh is the heat input, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

Let's calculate the work output of the first engine:

Qh1 = 3730 J (given)
Tc1 = 441 K (given)
Th1 = 926 K (given)

W1 = Qh1 * (1 - Tc1/Th1)
W1 = 3730 J * (1 - 441 K / 926 K)
W1 = 3730 J * (1 - 0.476)
W1 = 3730 J * 0.524
W1 = 1955.32 J

Now, the rejected heat from the first engine serves as the input for the second engine. The heat input for the second engine is the same as the heat output of the first engine:

Qh2 = W1 = 1955.32 J (from the previous calculation)
Tc2 = 441 K (given)
Th2 = 191 K (given)

Now, let's calculate the work output of the second engine:

W2 = Qh2 * (1 - Tc2/Th2)
W2 = 1955.32 J * (1 - 441 K / 191 K)
W2 = 1955.32 J * (1 - 2.305)
W2 = 1955.32 J * (-1.305)
W2 = -2549.06 J

Note that the work output of the second engine is negative because it is extracting additional work from the rejected heat of the first engine.

Finally, let's calculate the total work delivered by the two engines:

Total work = W1 + W2
Total work = 1955.32 J + (-2549.06 J)
Total work = 1955.32 J - 2549.06 J
Total work = -593.74 J

Therefore, the total work delivered by the two engines is -593.74 J.