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An air-conditioner in the airport of Timbuktu operates a cooling system using R-410a with a high pressure of 1500 kPa and a low pressure of 200 kPa. It is designed to cool the desert air from 45°C down to 15°C.

Find the cycle COP. Will the system work?

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.

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