Thermodynamics question about mass flow rate in an air conditioning unit?

In summary, the conversation discusses the process of mixing warm and fresh air in an air conditioning unit and estimating the temperature of the mixed air. The mass flowrate ratio is given as 1.6, and there is a question about whether the air standard assumptions are used for all heat engine and heat pump problems. The individual also mentions their attempt at solving the problem and suggests using a correlation for system design. They also mention using the specific heat of air to calculate the energy in and out, assuming constant specific heat and a high school-level difficulty.
  • #1
aero&astro
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1. In an air conditioning unit fresh air at 10°C is mixed with warm air at 30°C. If the mass flowrate ratio of warm to fresh air is 1.6, estimate the temperature at which the mixed air leaves the air conditioner. State any assumptions made.


and also do you always make the air standard assumptions for ALL heat engine and heat pump problems?


my attempt was mdot/mdot = flowrate ratio = change in temperature but then I don't think that makes sense, any help?
 
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  • #2
Such a correlation would aid in system design and allow the examination of a full range of refrigerant choices.


air conditioner
 
  • #3
One way to do it would be to may be calculate the energy in and energy out based off the specific heat of the air.
 
  • #4
Assume constant specific heat vs. temperature and it's a high school-level problem.
 
  • #5


I would approach this question by first considering the fundamental principles of thermodynamics. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the air conditioning unit is transferring heat energy from the warm air to the fresh air in order to maintain a desired temperature.

To answer the question, we need to use the equation for mass flow rate, which is mass flow rate = density x velocity x cross-sectional area. Assuming the cross-sectional area and velocity remain constant, the mass flow rate is directly proportional to the density of the air.

Given the mass flowrate ratio of 1.6, we can assume that for every 1.6 units of warm air, there is 1 unit of fresh air. This means that the density of the fresh air is lower than the density of the warm air. As the warm and fresh air mix, their densities will also mix, resulting in a final density that is between the two initial densities.

Now, we can use the equation for the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the work done by the system is negligible, so we can ignore it. The equation can be written as follows:

ΔU = Q - W

Where ΔU is the change in internal energy, Q is the heat added, and W is the work done by the system.

Assuming that the air conditioning unit is operating at steady state, the change in internal energy is zero. This means that the heat added to the system is equal to the heat removed from the warm air. We can express this as follows:

Q = m(warm) x Cp(warm) x (Tf - Tw)

Where m(warm) is the mass of the warm air, Cp(warm) is the specific heat capacity of the warm air, Tf is the final temperature of the mixed air, and Tw is the initial temperature of the warm air.

Similarly, we can express the heat removed from the warm air as follows:

Q = m(fresh) x Cp(fresh) x (Tf - Tf)

Where m(fresh) is the mass of the fresh air, Cp(fresh) is the specific heat capacity of the fresh air, and Tf is the final temperature of the
 

FAQ: Thermodynamics question about mass flow rate in an air conditioning unit?

What is the mass flow rate in an air conditioning unit?

The mass flow rate in an air conditioning unit refers to the amount of air that is moved through the system per unit of time. It is typically measured in kilograms per second (kg/s) or cubic meters per second (m3/s).

How is the mass flow rate calculated in an air conditioning unit?

The mass flow rate in an air conditioning unit can be calculated by dividing the volume flow rate by the density of the air. The volume flow rate can be measured using a flow meter, and the density of air can be determined from its temperature, pressure, and humidity.

What factors affect the mass flow rate in an air conditioning unit?

The mass flow rate in an air conditioning unit is affected by several factors, including the air temperature, pressure, humidity, and the size and design of the unit. Changes in these factors can impact the efficiency and performance of the system.

How does the mass flow rate impact the cooling capacity of an air conditioning unit?

The mass flow rate is directly related to the cooling capacity of an air conditioning unit. A higher mass flow rate means that more air is passing through the unit, which allows for a greater transfer of heat. This results in a higher cooling capacity and a more efficient system.

Can the mass flow rate be adjusted in an air conditioning unit?

Yes, the mass flow rate in an air conditioning unit can be adjusted by changing the fan speed or by adjusting the size of the unit's evaporator and condenser coils. However, it is important to note that the mass flow rate must be carefully balanced to ensure optimal performance and efficiency of the system.

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