At a nuclear power plant water at 8°c from a lake is used in a heat exchanger to condense spent steam at a temperature of 120°c,to water at 85°c before it is recycled to the reactor. If the cooling water returns to the lake at a temperature of 19°c,how many kilogram of water are needed per kilogram of steam ? Ignore the pressure change in steam.
To find out how many kilograms of water are needed per kilogram of steam, we can use the principle of energy conservation.
The heat lost by the steam equals the heat gained by the cooling water:
m1 * (h1 - h2) = m2 * (h3 - h4)
where:
m1 = mass of steam
m2 = mass of cooling water
h1 = enthalpy of steam at 120°C
h2 = enthalpy of water at 85°C
h3 = enthalpy of water at 19°C
h4 = enthalpy of water at 8°C
The enthalpy values can be obtained from the steam and water tables. For this calculation, we will consider the enthalpy values at the given temperatures (120°C, 85°C, 19°C, and 8°C).
Substituting the values into the equation, we have:
m1 * (h1 - h2) = m2 * (h3 - h4)
We know that the enthalpy of water at 8°C (h4) is greater than the enthalpy of water at 19°C (h3). So, the value of h3 - h4 will be negative.
Let's assume the mass of steam (m1) is 1 kg. We can solve for the mass of cooling water (m2):
1 * (h1 - h2) = m2 * (h3 - h4)
Solving for m2:
m2 = (h1 - h2) / (h4 - h3)
Substituting the enthalpy values into the equation will give us the required mass of cooling water per kilogram of steam.
Note: To obtain accurate values for enthalpy, it's recommended to refer to the steam tables or use appropriate software/tools for steam/water properties calculations.
To find out how many kilograms of water are needed per kilogram of steam at the nuclear power plant, we need to look at the energy balance equation.
The energy balance equation can be expressed as follows:
Mass(flow rate) of steam x Enthalpy(change in heat) of steam = Mass(flow rate) of water x Enthalpy(change in heat) of water
Let's calculate the enthalpy(change in heat) for both steam and water.
Enthalpy change for steam:
ΔH₁ = Specific heat capacity of steam x Mass of steam x (Final temperature of steam - Initial temperature of steam)
Enthalpy change for water:
ΔH₂ = Specific heat capacity of water x Mass of water x (Final temperature of water - Initial temperature of water)
For simplicity, we can assume the specific heat capacity of steam and water as constant values.
Given:
Initial temperature of steam (T₁) = 120°C
Final temperature of steam (T₂) = 85°C
Initial temperature of water (T₃) = 8°C
Final temperature of water (T₄) = 19°C
Let's calculate the enthalpy changes:
ΔH₁ = Specific heat capacity of steam x Mass of steam x (T₂ - T₁)
ΔH₂ = Specific heat capacity of water x Mass of water x (T₄ - T₃)
Since the specific heat capacities are constants, we can write an equation using the above information:
Specific heat capacity of steam x Mass of steam x (T₂ - T₁) = Specific heat capacity of water x Mass of water x (T₄ - T₃)
Now, let's rearrange the equation to solve for the mass of water (Mass of water/Mass of steam):
Mass of water/Mass of steam = (Specific heat capacity of steam x (T₂ - T₁))/(Specific heat capacity of water x (T₄ - T₃))
Plugging in the given values and the specific heat capacities of steam and water, we can calculate the mass of water needed per kilogram of steam.