A nuclear power plant has an electrical power output of 1200 MW and operates with an efficiency of 31%. If excess energy is carried away from the plant by a river with a flow rate of 1.0 multiplied by 10^6 kg/s, what is the rise in temperature of the flowing water?
To calculate the rise in temperature of the flowing water, we can use the principle of energy conservation. First, let's determine the amount of energy being carried away by the river.
Step 1: Calculate the total energy output of the power plant.
The electrical power output of the nuclear power plant is given as 1200 MW. However, the efficiency of the power plant is also provided as 31%.
Efficiency (ε) = Useful output energy / Total input energy
Therefore, the useful output energy can be calculated as:
Useful output energy = Efficiency × Total input energy
Total input energy = Electrical power output / Efficiency
Total input energy = 1200 MW / 0.31
Note: Convert MW to W by multiplying by 10^6, and divide by 0.31 to convert to the total input energy.
Step 2: Calculate the amount of energy carried by the river.
The energy carried away by the river can be determined using the equation:
Energy carried away = Mass flow rate of water × Specific heat of water × Temperature rise
Here, the mass flow rate of water is given as 1.0 × 10^6 kg/s.
Step 3: Calculate the rise in temperature.
Rearrange the equation to solve for the temperature rise:
Temperature rise = Energy carried away / (Mass flow rate of water × Specific heat of water)
Specific heat of water is approximately 4200 J/(kg°C).
Now that we have all the necessary information, let's calculate the rise in temperature of the flowing water.
Substituting the values into the equation:
Total input energy = (1200 × 10^6 W) / 0.31 ≈ 3870 × 10^6 J/s
Energy carried away = (1.0 × 10^6 kg/s) × (4200 J/(kg°C)) × ΔT
ΔT = Energy carried away / (Mass flow rate of water × Specific heat of water)
ΔT = (3870 × 10^6 J/s) / ((1.0 × 10^6 kg/s) × (4200 J/(kg°C)))
Calculating the value of ΔT will give us the rise in temperature of the flowing water.