Answer :
Note that the calculated COP is approximately 9.605, which is greater than 1. Therefore, the air-conditioning system using R-410a should work effectively to cool the desert air from 45°C to 15°C.
The coefficient of performance (COP) measures the efficiency of a refrigeration or heat pump system in providing cooling or heating.
Given:
- High pressure [tex]\( P_H = 1500 \)[/tex] kPa
- Low pressure [tex]\( P_L = 200 \)[/tex] kPa
- Initial temperature [tex]\( T_H = 45 \)[/tex] °C
- Final temperature [tex]\( T_L = 15 \)[/tex] °C
Let's calculate the COP of the air-conditioning system using the Carnot refrigeration cycle equation:
1. Convert temperatures from Celsius to Kelvin:
[tex]\[ T_H = 45 + 273.15 = 318.15 \, \text{K} \][/tex]
[tex]\[ T_L = 15 + 273.15 = 288.15 \, \text{K} \][/tex]
2. Calculate the COP using the equation:
[tex]\[ \text{COP} = \frac{T_L}{T_H - T_L} \][/tex]
[tex]\[ \text{COP} = \frac{288.15 \, \text{K}}{318.15 \, \text{K} - 288.15 \, \text{K}} \][/tex]
[tex]\[ \text{COP} = \frac{288.15}{30} \][/tex]
[tex]\[ \text{COP} = 9.605 \][/tex]
The calculated COP is approximately 9.605, which is greater than 1.
Hence, it is correct to state that the air-conditioning system using R-410a should work effectively to cool the desert air from 45°C to 15°C.
