Question

A heat engine with efficiency 35 percent of a Carnot engine operating between a high temperature of 86 degrees Celsius and a low temperature of -66 degrees Celsius takes in 165,000 Joules of heat each cycle. How many cycles are required to do 8,900,000 Joules of work

Answer 1

The heat engine has an efficiency of 35%. The number of cycles required to do 8,900,000 J of work is approximately 44 cycles.

Step-by-step explanation:

The efficiency of a heat engine is given by the formula:

Efficiency = 1 - (Tc/Th)

Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. In this case, the efficiency of the heat engine is given as 35%, which is equivalent to 0.35.

Using the formula, we can calculate the temperature of the hot reservoir:

0.35 = 1 - (-66 - Tc)/(86 - Tc)

Simplifying the equation, we find that Tc is equal to -73.6 degrees Celsius.

Now, we can determine the temperature of the hot reservoir:

Th = (-66 - Tc)/0.35 + Tc = 97.7 degrees Celsius

Next, we can calculate the amount of heat absorbed by the engine per cycle:

Qh = Efficiency * Qc = 0.35 * 165,000 J = 57,750 J

To determine the number of cycles required to do 8,900,000 J of work, we can use the equation:

Work = Efficiency * Qh * N

Solving for N, we find:

N = Work / (Efficiency * Qh) = 8,900,000 J / (0.35 * 57,750 J) ≈ 44 cycles