Answer:
Explanation:
Given that:
<u>At state 1:</u>
Pressure P₁ = 20 bar
Volume V₁ = 0.03 ![\mathbf{m^{3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%5E%7B3%7D%7D)
From the tables at saturated vapour;
Temperature T₁ = 212.4⁰ C ;
= 0.0996
/ kg
The mass inside the cylinder is m = 0.3 kg, which is constant.
The specific internal energy u₁ = ug₁ = 2599.2 kJ/kg
<u>At state 2:</u>
Temperature T₂ = 200⁰ C
Since the 1 - 2 occurs in an isochoric process v₂ = v₁ = 0.099
/ kg
From temperature T₂ = 200⁰ C
Since
, the saturated pressure at state 2 i.e. P₂ = 15.5 bar
Mixture quality ![x_2 = \dfrac{v_2-vf_2}{vg_2 -vf_2}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cdfrac%7Bv_2-vf_2%7D%7Bvg_2%20-vf_2%7D)
![x_2 = \dfrac{(0.099-0.0016)m^3/kg}{(0.127 -0.0016) m^3/kg}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cdfrac%7B%280.099-0.0016%29m%5E3%2Fkg%7D%7B%280.127%20-0.0016%29%20m%5E3%2Fkg%7D)
![x_2 = \dfrac{(0.0974)m^3/kg}{(0.1254) m^3/kg}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cdfrac%7B%280.0974%29m%5E3%2Fkg%7D%7B%280.1254%29%20m%5E3%2Fkg%7D)
![\mathsf{x_2 =0.78}](https://tex.z-dn.net/?f=%5Cmathsf%7Bx_2%20%3D0.78%7D)
At temperature T₂, the specific internal energy
, also ![ug_2 = 2594.3 \ kJ/kg](https://tex.z-dn.net/?f=ug_2%20%3D%202594.3%20%5C%20kJ%2Fkg)
Thus,
![u_2 = uf_2 + x_2 (ug_2 -uf_2)](https://tex.z-dn.net/?f=u_2%20%3D%20uf_2%20%2B%20x_2%20%28ug_2%20-uf_2%29)
![u_2 =850.6 +0.78 (2594.3 -850.6)](https://tex.z-dn.net/?f=u_2%20%3D850.6%20%20%2B0.78%20%282594.3%20-850.6%29)
![u_2 =850.6 +1360.086](https://tex.z-dn.net/?f=u_2%20%3D850.6%20%20%2B1360.086)
![u_2 =2210.686 \ kJ/kg](https://tex.z-dn.net/?f=u_2%20%3D2210.686%20%5C%20kJ%2Fkg)
<u>At state 3:</u>
Temperature ![T_3=T_2 = 200 ^0 C ,](https://tex.z-dn.net/?f=T_3%3DT_2%20%3D%20200%20%5E0%20C%20%2C)
![V_3 = 2V_1 = 0.06 \ m^3](https://tex.z-dn.net/?f=V_3%20%3D%202V_1%20%3D%200.06%20%5C%20m%5E3)
Specific volume ![v_3 = 0.2 \ m^3/kg](https://tex.z-dn.net/?f=v_3%20%3D%200.2%20%20%5C%20m%5E3%2Fkg)
Thus;
,
SInce
, therefore, the phase is in a superheated vapour state.
From the tables of superheated vapour tables; at
and T₃ = 200⁰ C
The pressure = 10 bar and v =0.206 ![\ m^3/kg](https://tex.z-dn.net/?f=%5C%20m%5E3%2Fkg)
The specific internal energy
at the pressure of 10 bar = 2622.3 kJ/kg
The changes in the specific internal energy is:
![u_2-u_1](https://tex.z-dn.net/?f=u_2-u_1)
= (2210.686 - 2599.2) kJ/kg
= -388.514 kJ/kg
≅ - 389 kJ/kg
![u_3-u_2](https://tex.z-dn.net/?f=u_3-u_2)
= (2622.3 - 2210.686) kJ/kg
= 411.614 kJ/kg
≅ 410 kJ/kg
We can see the correct sketches of the T-v plot showing the diagrammatic expression in the image attached below.