An air conditioner takes outside air at 35°C and cools it to 15°C at a rate of 1 kg/s. Estimate the amount of power needed to do this. Recalculate the needed power if it is put in recirculation mode using inside air at 24°C and cools that to 15°C.

Q=20.1kW

recirculation mode=Q=9.045kW

Explanation:

Hi!

To solve this problem you must use the first law of thermodynamics that establishes the energy that enters a system is the same that must come out. Given the above we have the following equation

Q = mCp (T2-T1)

WHERE

Q = Heat removed to air

m = mass air flow = 1kg / s

Cp = specific heat of air = 1.005KJ / kg °C

T2 = air inlet temperature

T1 = air outlet temperature=15°C.

for the first case

Q = (1kg/s) (1.005KJ/kg°C) (35°C-15°C)

Q=20.1kW

for the second case (recirculation mode)

Q = (1kg/s) (1.005KJ/kg°C) (24°C-15°C)

Q=9.045kW