Answer:
(1) 5.74
(2) 5.09
(3) 3.05×10⁻⁵ kg/s
(4) 0.00573 kW
Explanation:
The parameters given are;
Working temperature,
= -15°C = 258.15 K
Temperature of the cooling water,
= 30°C = 303.15 K
(1) The Carnot coefficient of performance is given as follows;
![\gamma_{Max} = \dfrac{T_C}{T_H - T_C} = \dfrac{258.15}{303.15 - 258.15} = 5.74](https://tex.z-dn.net/?f=%5Cgamma_%7BMax%7D%20%3D%20%5Cdfrac%7BT_C%7D%7BT_H%20-%20T_C%7D%20%20%3D%20%20%5Cdfrac%7B258.15%7D%7B303.15%20-%20258.15%7D%20%20%20%3D%205.74)
(2) For ammonia refrigerant, we have;
![h_2 = h_g = 1466.3 \ kJ/kg](https://tex.z-dn.net/?f=h_2%20%3D%20h_g%20%3D%201466.3%20%5C%20kJ%2Fkg)
![h_3 = h_f = 322.42 \ kJ/kg](https://tex.z-dn.net/?f=h_3%20%3D%20h_f%20%3D%20322.42%20%5C%20kJ%2Fkg)
![h_4 = h_3 = h_f = 322.42 \ kJ/kg](https://tex.z-dn.net/?f=h_4%20%3D%20h_3%20%3D%20h_f%20%3D%20322.42%20%5C%20kJ%2Fkg)
s₂ = s₁ = 4.9738 kJ/(kg·K)
0.4538 + x₁ × (5.5397 - 0.4538) = 4.9738
∴ x₁ = (4.9738 - 0.4538)/(5.5397 - 0.4538) = 0.89
![h_1 = h_{f1} + x_1 \times h_{gf}](https://tex.z-dn.net/?f=h_1%20%3D%20h_%7Bf1%7D%20%2B%20x_1%20%5Ctimes%20h_%7Bgf%7D)
h₁ = 111.66 + 0.89 × (1424.6 - 111.66) = 1278.5 kJ/kg
![\gamma = \dfrac{h_1 - h_4}{h_2 - h_1}](https://tex.z-dn.net/?f=%5Cgamma%20%3D%20%5Cdfrac%7Bh_1%20-%20h_4%7D%7Bh_2%20-%20h_1%7D)
![\gamma = \dfrac{1278.5 - 322.42}{1466.3 - 1278.5} = 5.09](https://tex.z-dn.net/?f=%5Cgamma%20%3D%20%5Cdfrac%7B1278.5%20-%20322.42%7D%7B1466.3%20-%201278.5%7D%20%3D%205.09)
(3) The circulation rate is given by the mass flow rate,
as follows
![\dot m = \dfrac{Refrigeration \ capacity}{Refrigeration \ effect \ per \ unit \ mass}](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%20%5Cdfrac%7BRefrigeration%20%5C%20capacity%7D%7BRefrigeration%20%5C%20effect%20%5C%20per%20%5C%20unit%20%5C%20mass%7D)
The refrigeration capacity = 105 kJ/h
The refrigeration effect, Q = (h₁ - h₄) = (1278.5 - 322.42) = 956.08 kJ/kg
Therefore;
![\dot m = \dfrac{105}{956.08} = 0.1098 \ kg/h](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%20%5Cdfrac%7B105%7D%7B956.08%7D%20%20%3D%200.1098%20%5C%20kg%2Fh)
= 0.1098 kg/h = 0.1098/(60*60) = 3.05×10⁻⁵ kg/s
(4) The work done, W = (h₂ - h₁) = (1466.3 - 1278.5) = 187.8 kJ/kg
The rating power = Work done per second = W×![\dot m](https://tex.z-dn.net/?f=%5Cdot%20m)
∴ The rating power = 187.8 × 3.05×10⁻⁵ = 0.00573 kW.