18. (II) At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate ehat input of the second. Th eoperating temeprautres of the first are 680 degrees C and 430 degrees C, and of the second 415 degrees C and 280 degrees C. If the heat of combuston of coal is 2.8 E8 J/kg, at what rate msut coal be burned if the plant is to put out 900 MW of power. Assume the efficiency of the engines is 65 percent of the ideal (Carnot) efficiency.

Question

18. (II) At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate ehat input of the second. Th eoperating temeprautres of the first are 680 degrees C and 430 degrees C, and of the second 415 degrees C and 280 degrees C. If the heat of combuston of coal is 2.8 E8 J/kg, at what rate msut coal be burned if the plant is to put out 900 MW of power. Assume the efficiency of the engines is 65 percent of the ideal (Carnot) efficiency.

Can you tell me if i did this right because I got 640 Kg every second

Answer 1

To calculate the rate at which coal must be burned, we can use the following equation:

Power output = Efficiency * Heat input

First, let's calculate the heat input:

For the first steam engine:
Temperature of heat input (T1) = 680 degrees C
Temperature of heat output (T2) = 430 degrees C

For the second steam engine:
Temperature of heat input (T3) = 415 degrees C
Temperature of heat output (T4) = 280 degrees C

Next, we need to calculate the efficiency of the engines:

Efficiency = (Actual efficiency / Ideal efficiency) * 100

Given that the actual efficiency is 65% of the ideal (Carnot) efficiency, we can calculate:

Actual efficiency = 0.65 * Ideal efficiency

Since the ideal efficiency is given by the Carnot efficiency, we can use the formula:

Ideal efficiency = 1 - (T4 / T3)

Now we can calculate the efficiency:

Actual efficiency = 0.65 * (1 - (T4 / T3))

Next, let's calculate the heat input:

Heat input = Power output / Efficiency

Power output = 900 MW

Remember to convert MW to J/s:

1 MW = 1,000,000 J/s

Now we can calculate the rate at which coal must be burned:

Rate of coal burned = Heat input / Heat of combustion of coal

Heat of combustion of coal = 2.8 E8 J/kg

Finally, we can put all the values together to find the rate at which coal must be burned:

Rate of coal burned = (Power output / Efficiency) / Heat of combustion of coal

Remember to convert the rate to kg/s:

1 kg/s = 1,000 g/s

Make sure to perform all the necessary unit conversions and calculations accurately to get the correct answer.