A nuclear power plant has an electrical power output of 1900 MW and operates with an efficiency of 32%. If excess energy is carried away from the plant by a river with a flow rate of 1.0 106 kg/s, what is the rise in temperature of the flowing water?
°C
To calculate the rise in temperature of the flowing water, we need to use the concept of energy conservation.
First, let's determine the amount of energy the power plant produces. The electrical power output of the power plant is given as 1900 MW. However, since the plant operates with an efficiency of 32%, only 32% of this energy is converted into useful electrical energy.
So, we need to calculate the amount of useful electrical energy produced by the power plant:
Useful electrical energy = (Efficiency) * (Total electrical power output)
= (0.32) * (1900 MW)
= 608 MW
Next, we need to find the rate at which energy is carried away by the river. This can be determined by multiplying the flow rate of the river by the specific heat capacity of water and the change in temperature.
Rate of energy carried away = (Mass flow rate) * (Specific heat capacity) * (Change in temperature)
Given:
Flow rate of the river = 1.0 * 10^6 kg/s
Specific heat capacity of water = 4186 J/kg°C (approximate value)
To find the change in temperature, we rearrange the equation:
Change in temperature = (Rate of energy carried away) / ((Mass flow rate) * (Specific heat capacity))
Plugging in the values:
Change in temperature = (608 * 10^6 J/s) / ((1.0 * 10^6 kg/s) * (4186 J/kg°C))
Simplifying the equation:
Change in temperature = 145.59 °C
Therefore, the rise in temperature of the flowing water is approximately 145.59 °C.