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