a. A power plant burns coal and generates an average of 610.0 Megawatts (MW) of electrical power while discharging 915.00 MW as waste heat. Find the total electrical energy generated by the plant in a 30-day period.
b. Coals vary a lot in their energy content. The energy released by the burning of coal is typically between 23 and 33 Mega Joules per kg of coal. The power plant above uses coal rated at 33.0 MJ/kg to heat the boilers. Some of that heat is converted to electrical energy, but most is waste heat discharged into the environment. Assume that it takes about 2.32 kg of oxygen to burn 1 kg of coal (The actual amount varies with the type coal). Find the total mass of the reagents used in operating for 30 days.
610MW = 610MJ/s.
a. Energy = 610MJ/s * 3600s/h * 24h/day * 30days = 1.581*10*9 MJ.
b. 1.58e9/33 = 4.8e7 kg coal for power. But only 33% efficient so total coal = 4.8e7 +(1.5*4.8e7) = 1.2e8 kg coal.
Add 2.8e8 kg oxygen.
Total reagents = 4.0e8
To solve these problems, we'll need to calculate the total electrical energy generated by the power plant in a 30-day period and the total mass of the reagents used.
a. To find the total electrical energy generated by the power plant in a 30-day period, we need to calculate the energy generated per day and then multiply it by the number of days.
Step 1: Calculate the energy generated per day:
Power generated = 610.0 MW
Waste heat discharged = 915.00 MW
The total energy generated per day can be found by subtracting the waste heat from the power generated:
Energy generated per day = Power generated - Waste heat
Energy generated per day = 610.0 MW - 915.00 MW
Step 2: Convert the power values to energy by multiplying by the number of hours in a day:
Energy generated per day = (610.0 MW - 915.00 MW) * 24 hours
Step 3: Convert the energy from hours to kilowatt-hours (kWh):
Energy generated per day = (610.0 MW - 915.00 MW) * 24 hours * 1000 kWh/MWh
Step 4: Calculate the total electrical energy generated in a 30-day period:
Total electrical energy generated = Energy generated per day * 30 days
Now, you can substitute the given values into the equation to find the answer.
b. To find the total mass of the reagents used in operating for 30 days, we need to calculate the mass of coal burned per day and then multiply it by the number of days.
Step 1: Calculate the mass of coal burned per day:
Energy released by burning coal = 33.0 MJ/kg
Mass of oxygen required to burn 1 kg of coal = 2.32 kg
The mass of coal burned per day can be found by dividing the energy generated per day by the energy released by burning coal:
Mass of coal burned per day = Energy generated per day / (Energy released by burning coal * Mass of oxygen required to burn 1 kg of coal)
Step 2: Calculate the total mass of coal burned in a 30-day period:
Total mass of coal burned = Mass of coal burned per day * 30 days
Now, you can substitute the given values into the equation to find the answer.