Respuesta :
Based on the calculations, the amount of heat transferred is equal to 2,317 kJ.
Given the following data:
Volume of tank = 0.4 m³.
Initial pressure = 160 kPa.
Final pressure = 600 kPa.
Initial quality, x = 40% = 0.4
How to calculate the amount of heat transferred?
From the superheat table A-12, the specific volumes of the saturated liquid and vapor at 160 kPa are:
- Vf(160 kPa) = 0.0007437 m³/kg.
- Vg(160 kPa) = 0.12348 m³/kg.
Next, we would determine the initial specific volume by using this formula:
V₁ = (1 - x)Vf + xVg
V₁ = (1 - 0.4)0.0007437 + (0.4)0.12348
V₁ = 0.049838 m³/kg.
Also, we would find the mass of this refrigerant at the initial state by using this equation:
m = V/V₁
m = 0.4/0.049838
Mass, m = 8.03 kg.
From the superheat table A-12, the internal energy of the saturated liquid and vapor at 160 kPa are:
- Uf(160 kPa) = 31.09 kJ/kg.
- Ug(160 kPa) = 221.35 kJ/kg.
At the initial state, we would find U₁ from the quality:
U₁ = (1 - x)Uf + xUg
U₁ = (1 - 0.4)31.09 + (0.4)221.35
U₁ = 107.19 kJ/kg.
From the superheat table A-13, the final specific volume and internal energy of the saturated liquid and vapor at 600 kPa are:
- Vf = 0.057006 m³/kg.
- Uf = 367.81 kJ/kg.
At the final state, we would find U₂ by extrapolating with the last two points in the table:
[tex]U_2 = 357.96 + (\frac{367.81 \; - \; 357.96}{0.057006\;-\;0.055522}) \times (0.049838\;-\;0.055522)\\\\U_2 = 357.96 + (\frac{9.85}{0.001484}) \times (-0.005684)\\\\U_2 = 357.96 + 37.73\\\\[/tex]
U₂ = 395.69 kJ/kg.
Now, we can calculate the amount of heat transferred:
Q = m(U₂ - U₁)
Q = 8.03(395.69 - 107.19)
Q = 8.03(288.5)
Q = 2,316.66 ≈ 2,317 kJ.
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