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Old Sep 24th 2016, 08:12 AM   #1
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Join Date: Sep 2016
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Talking Practical Thermodynamics problem

Hi guys! I've been spending a lot of time lately trying to answer this problem but I always end up getting confused on how to set my main starting equation and I really need help with it.

How much time does it take for an air conditioner to cool a room of volume 204 cubic meter, from 30 C to 21 C? The cooling capacity of the AC is 25,000 kJ/hr. assume that the room is well insulated.

So based on how I understand an AC's behavior, it gets air from the room (higher temp), then releases cooler air but of the same mass flow rate (right?)
and so, in turn, the air that goes out of the AC is the air that goes into the room. So basically the air is just in cycle.

How do I set up my starting equation? Do I really need the cooling capacity of the AC to solve this problem? I'd really appreciate anyone's help
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Old Sep 24th 2016, 11:32 AM   #2
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That's not quite correct. The air conditioner take air from both the outside and inside, cools part of the air while dumping that heat into another part of the air, the exhausts the cooled air to the inside, the warmed air to the inside. Here, you say that the air conditioner has cooling capacity 25000 KJ per hour. Okay, if you cool one cubic meter of air from 30 C to 21 C, how much work does that require? (Ignoring inefficiencies, how much heat energy has to be removed?) For a 204 cubic meter room, multiply that number by 204. That gives the total energy, in Joules, required. divide by 25000 to see how many hours that will take.
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Old Sep 25th 2016, 10:23 AM   #3
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attached is my rough solution I started with the general equation and to arrive in your said solution, there's still mass flow out even tho the room is well insulated? so this probably is the mass flow going into the aircon right? then this mass flow is also equal to the mass flow going out of the aircon (meaning going into the room).

How come my answer is too small? I expected it to be like around 30 minutes. is my solution right?
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Old Oct 7th 2016, 12:45 PM   #4
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Some A/Cs are recirculatory and have a cooling coil which ejects heat via some other coolant. In this case you look at the mass of air in the cube by taking the volume and multiplying it by the density of (assumed dry) air at 30oC. This mass doesnt change for the recirculatory system. If the cooling capacity is 25000 KJ/hr or 6.94 kW then you can calcualte the energy required to cool the mass of air down by assuming a constant heat capacity over the temperature change. You are also assuming that the heat transfer from the air to the coolant is similar across the temperature range ( i.e the coolant is much cooler than 21oC). If you make these assumptions then the calculation is a trivial calculation from Q = MCpDT and you look at how long the A/C will require by dividing the heat required by the heat capacity or power of the A/C unit.

so 237 kg of air, Cp = 1.005 kJ/kg K, DT =9, 2144 KJ required perhaps 5 minutes cooling time??
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