Answer:
The Entropy generated by the steam = 2.821 kJ/K
Explanation:
Total volume of container = 5m³
Heat transfer does not exist between system and surrounding, dQ = 0
At the first chamber, temperature of water at saturated liquid is 300°C
From the steam table:
Specific enthalpy of saturated liquid at 300°C , ![h_{f} = 1344.8 kJ/kg](https://tex.z-dn.net/?f=h_%7Bf%7D%20%3D%201344.8%20kJ%2Fkg)
Specific internal energy of saturated liquid at 300°C,
1332.7 kJ/kg
For closed system, the first law of thermodynamics state that:
dQ = dw + dU..................(1)
work done for free expansion, dw =0
0 = 0 + dU
dU = 0 , i.e. U₁ = U₂
At the second chamber,
The final pressure, P₂ = 50 kPa
From the steam table, at P₂ = 50 kPa,
= 340.49 kJ/kg
![(U_{fg} )_{2} = 2142.7 kJ/kg](https://tex.z-dn.net/?f=%28U_%7Bfg%7D%20%29_%7B2%7D%20%3D%20%202142.7%20kJ%2Fkg)
Let the dryness fraction at the second chamber = x
![U_{2} = U_{f2} + U_{fg2}](https://tex.z-dn.net/?f=U_%7B2%7D%20%3D%20U_%7Bf2%7D%20%2B%20U_%7Bfg2%7D)
Since U₁ = U₂
1332.7 = 340.49 + x2140.7
Dryness fraction, x = 0.463
From steam table, the specific volume is, ![u_{f2} = 0.00103 m^{3} /kg\\](https://tex.z-dn.net/?f=u_%7Bf2%7D%20%3D%200.00103%20m%5E%7B3%7D%20%2Fkg%5C%5C)
![u_{2} = u_{f2} + xu_{fg2}](https://tex.z-dn.net/?f=u_%7B2%7D%20%3D%20u_%7Bf2%7D%20%2B%20xu_%7Bfg2%7D)
![u_{2} = 0.00103 + 0.463(3.2393)\\u_{2} = 1.5 m^{3} /kg\\](https://tex.z-dn.net/?f=u_%7B2%7D%20%3D%200.00103%20%2B%200.463%283.2393%29%5C%5Cu_%7B2%7D%20%3D%201.5%20m%5E%7B3%7D%20%2Fkg%5C%5C)
![u_{2} = \frac{v_{2} }{m_{2} }](https://tex.z-dn.net/?f=u_%7B2%7D%20%3D%20%5Cfrac%7Bv_%7B2%7D%20%7D%7Bm_%7B2%7D%20%7D)
V₂ = 5 m³
1.5 = 5/m₂
m₂ = 3.33 kg
At 300°C ![S_{1} = S_{f} = 3.2548 kJ/kg-k\\](https://tex.z-dn.net/?f=S_%7B1%7D%20%3D%20S_%7Bf%7D%20%3D%203.2548%20kJ%2Fkg-k%5C%5C)
![S_{2} = S_{f2} + xS_{fg2}](https://tex.z-dn.net/?f=S_%7B2%7D%20%3D%20S_%7Bf2%7D%20%2B%20xS_%7Bfg2%7D)
From the steam table,
![S_{f2} = 1.0912 kJ/kg-k\\S_{fg2} = 6.5019 kJ/kg-k\\S_{2} = 1.0912 + 0.463(6.5019)\\S_{2} = 4.102 kJ/kg-k](https://tex.z-dn.net/?f=S_%7Bf2%7D%20%3D%201.0912%20kJ%2Fkg-k%5C%5CS_%7Bfg2%7D%20%3D%206.5019%20kJ%2Fkg-k%5C%5CS_%7B2%7D%20%3D%201.0912%20%2B%200.463%286.5019%29%5C%5CS_%7B2%7D%20%3D%204.102%20kJ%2Fkg-k)
Therefore the entropy generated will be :
Entropy = mass* (S₂ - S₁)
Entropy = 3.33* (4.102 - 3.2548)
Entropy = 2.821 kJ/K