A town is planning on using the water flowing through a river at a rate of 4.9 106 kg/s to carry away the heat from a new power plant. Environmental studies indicate that the temperature of the river should only increase by 0.50° C. The maximum design efficiency for this plant is 32.0%. What is the maximum possible power this plant can produce?
Thermal power is rate of thermal energy.
P = (thermal energy) / (time) = Q/t =
= m•c•ΔT / t
= (m/t) • (c) • (ΔT)
Here m/t = 4.9•10^6 kg/s
c = specific heat of water = 4186 J/kg•C
ΔT = change in the temperature = 0.50 °C
Substituting all these values in the equation we get
P = 4.9•10^6 •4186 •0.50 =
= 1.02557•10^10 W =10.2557 GW.
Ans. 0.32 •10.2557 GW = 3.28GW
Thermal power is rate of thermal energy.
P = (thermal energy) / (time) = Q/t =
= m•c•ΔT / t
= (m/t) • (c) • (ΔT)
Here m/t = 4.9•10^6 kg/s
c = specific heat of water = 4186 J/kg•C
ΔT = change in the temperature = 0.50 °C
Substituting all these values in the equation we get
P = 4.9•10^6 •4186 •0.50 =
= 1.02557•10^10 W =10.2557 GW.
Ans. 0.32 •10.2557 GW = 3.28GW
To determine the maximum possible power this plant can produce, we can use the formula:
Power = Heat Transfer Rate / Thermal Efficiency
First, let's find the heat transfer rate. The heat transfer rate is calculated using the equation:
Heat Transfer Rate = Mass Flow Rate * Specific Heat Capacity * Temperature Change
Given values:
Mass Flow Rate = 4.9 * 10^6 kg/s
Specific Heat Capacity of water = 4186 J/kg⋅K
Temperature Change = 0.50°C
Substituting the values into the equation, we have:
Heat Transfer Rate = (4.9 * 10^6 kg/s) * (4186 J/kg⋅K) * (0.50°C)
To convert the temperature change from °C to K, we need to add 273.15:
Temperature Change = (0.50°C + 273.15) K
Now, we can calculate the heat transfer rate:
Heat Transfer Rate = (4.9 * 10^6 kg/s) * (4186 J/kg⋅K) * (0.50°C + 273.15) K
Next, we need to calculate the thermal efficiency. The thermal efficiency is given as 32.0%, which can be written as 0.32 in decimal form.
Now we have all the necessary information to calculate the maximum possible power:
Power = Heat Transfer Rate / Thermal Efficiency
Substituting the values, we get:
Power = [(4.9 * 10^6 kg/s) * (4186 J/kg⋅K) * (0.50°C + 273.15) K] / 0.32
Calculate the values within the brackets first:
Power = [(4.9 * 10^6 kg/s) * (4186 J/kg⋅K) * (273.65 K)] / 0.32
Now multiply the result by the coefficient outside the brackets:
Power = (4.9 * 10^6 kg/s) * (4186 J/kg⋅K) * (273.65 K) / 0.32
Solving this equation will give us the maximum possible power that the plant can produce.