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Answer :
The amount of power needed to operate the air-conditioner is approximately 20.1 kW. None of the options provided match this value, so the correct answer is not among the options provided.
To estimate the amount of power needed to operate the air-conditioner, we can use the following formula:
Power = mass flow rate * specific heat capacity * temperature difference
Given:
Mass flow rate of air (m) = 1 kg/s
Temperature of cooled air (T2) = 15°C = 15 + 273.15 = 288.15 K
Temperature of outside air (T1) = 35°C = 35 + 273.15 = 308.15 K
Specific heat capacity of air at constant pressure (Cp) = 1005 J/(kg·K) (approximate value for air)
Using the formula, the power can be calculated as follows:
Power = m * Cp * (T1 - T2)
Power = 1 kg/s * 1005 J/(kg·K) * (308.15 K - 288.15 K)
Power = 1 kg/s * 1005 J/(kg·K) * 20 K
Power = 20,100 J/s = 20.1 kW
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