A steam-electric power plant delivers 900 MW of electric power. The surplus heat is exhausted into a river with a flow of 2.91×105 kg/s, causing a change in temperature of 1.07 oC.
A. What is the efficiency of the power plant?
B. What is the rate of the thermal source?
MY WORK:
I know that 900 MW is 9x10^8 W. I just am having trouble finding an equation that relates at all to this question... I found a question that was similar but was looking for the temperature change and not the efficiency and tried to re-word their equation but it did not work:
power in watts / efficiency / 4.18 cal/s / flow = change in temp
I got 69.1 as the percent and it did not work, also tried 30.9 and it did not work.
P(lost) = mcΔT/t
From that you can determine efficiency.
How? I don't have mass or time, and I supposed to use 2.91×10^5 kg/s? The problem also does not mention a liquid or anything so how do I know what c to use??
To solve this problem, we need to use the concept of energy efficiency and the equation for heat transfer.
A. To find the efficiency of the power plant, we can use the formula:
Efficiency = (Useful output energy / Input energy) x 100
In this case, the useful output energy is the electric power generated by the power plant, which is given as 900 MW. We need to convert this to joules per second (Watts).
1 MW = 1,000,000 Watts
So, 900 MW = 900,000,000 Watts
Now, we can find the input energy using the equation:
Input energy = Useful output energy + Waste energy
The waste energy, in this case, is the heat exhausted into the river. To calculate the waste energy, we can use the equation:
Waste energy = mass flow rate x specific heat x temperature change
The mass flow rate is given as 2.91 × 10^5 kg/s, and the temperature change is given as 1.07 °C. However, we need to convert °C to Kelvin (K) since temperature must be in Kelvin in this calculation.
The specific heat of water is approximately 4.18 J/g·°C or 4.18 kJ/kg·K.
Now, we can substitute these values into the equation for waste energy:
Waste energy = (2.91 × 10^5 kg/s) x (4.18 kJ/kg·K) x (1.07 K)
Now, we can substitute the calculated values into the equation for input energy:
Input energy = Useful output energy + Waste energy
Input energy = (900,000,000 Watts) + [(2.91 × 10^5 kg/s) x (4.18 kJ/kg·K) x (1.07 K)]
Now, we can substitute these values into the equation for efficiency:
Efficiency = (Useful output energy / Input energy) x 100
Efficiency = (900,000,000 Watts / (900,000,000 Watts + [(2.91 × 10^5 kg/s) x (4.18 kJ/kg·K) x (1.07 K)])) x 100
Now, we can calculate the efficiency of the power plant using a calculator or a program.
B. To find the rate of the thermal source, we can use the formula:
Rate of thermal source = Waste energy / Time
The waste energy value can be calculated using the equation we used in part A. To find the time value, we need additional information from the question. If the time is not given, we cannot directly determine the rate of the thermal source.
Please provide the time duration for which the waste energy is being exhausted into the river, and I can assist you in calculating the rate of the thermal source.