Saturated liquid at a higher pressure P1 having h11 = 1000 kJ/kg is th...
In throttling process enthalpy remains constant.
h1 = h2
1000 = 800 + x(2800 — 800)
x = 0.1.
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Saturated liquid at a higher pressure P1 having h11 = 1000 kJ/kg is th...
To find the dryness fraction of the vapor after throttling, we can use the First Law of Thermodynamics for a control volume. The equation is given as:
Δh = h2 - h1 = (v2^2 - v1^2) / 2 + g(z2 - z1) + Q - W
Where:
Δh = change in enthalpy
h2 = enthalpy of the saturated vapor
h1 = enthalpy of the saturated liquid
v2 = specific volume of the saturated vapor
v1 = specific volume of the saturated liquid
g = acceleration due to gravity
z2 = height of the control volume at P2
z1 = height of the control volume at P1
Q = heat transfer
W = work done
In this case, the system is undergoing throttling, which means there is no heat transfer or work done. Therefore, the equation simplifies to:
Δh = h2 - h1 = (v2^2 - v1^2) / 2 + g(z2 - z1)
Since the system is at a higher pressure P1 initially, the saturated liquid at P1 is throttled to a lower pressure P2. This means that the specific volume of the saturated liquid remains the same, but the specific volume of the saturated vapor changes.
Given:
h1 = 1000 kJ/kg
v1 = specific volume of saturated liquid = constant
h2 = 2800 kJ/kg
v2 = specific volume of saturated vapor after throttling
Substituting the given values into the equation:
2800 - 1000 = (v2^2 - v1^2) / 2
Rearranging the equation:
v2^2 = 2 * (2800 - 1000) + v1^2
v2^2 = 3600 + v1^2
Now, we can use the definition of dryness fraction (x) to find the specific volume of the mixture:
v = x * v_g + (1 - x) * v_f
Where:
v = specific volume of the mixture
x = dryness fraction
v_g = specific volume of the saturated vapor
v_f = specific volume of the saturated liquid
Given:
v_f = constant
v_g = v2 (specific volume of saturated vapor after throttling)
Substituting the given values into the equation:
v = x * v2 + (1 - x) * v1
Since v1 is constant, the equation simplifies to:
v = x * v2 + v1 - x * v1
Now, we can substitute this equation into the previous equation:
v2^2 = 3600 + (x * v2 + v1 - x * v1)^2
Expanding and rearranging the equation:
v2^2 = 3600 + x^2 * (v2 - v1)^2 + v1^2 - 2 * x * v1 * (v2 - v1)
Simplifying the equation:
v2^2 - x^2 * (v2 - v1)^2 - v1^2 + 2 * x * v1 * (v2 - v1) - 3600 = 0
This equation is a quadratic equation in terms of x. We
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