Thermodynamics refrigeration Problem

[Bebalo]

Hey, I'm having a bit of trouble with a Thermo problem on a homework assignment. The problem is:

6-138 (Thermodynamics: An Engineering Approach, 5th Edition)

The drinking water needs of a production facility with 20 employees is to be met by a bobbler type water fountain. The refrigerated water fountain is to cool water from 22 C to 8 C and supply cold water at a rate of 0.4 L per hour per person. Heat is transferred to the reservoir from the surroundings at 25 C at a rate of 45 W. If the COP of the refrigeration system is 2.9, determine the size of the compressor, in W, that will be suitable for the refrigeration system of this water cooler.



Using the density of water, I first determined the mass flow rate of the water to be 0.00222 kg/s.

I know that I can use COP=(Ql)/(Qh-Ql)=(Ql)/(Win).

I think the next step I need to take is to set up an energy balance (Sum Ein = Sum Eexit) but I'm not entirely sure how to complete this step.

Thanks in advance for the help.

 

[Astronuc]

The rate of Q_l is $\dot{m}\,c_p\,\Delta{T}$ ,
and you know COP, and heat out to environment, 45 W.

 

[piercas]

Hello there,

I can see that you have already made some good progress in solving this thermodynamics refrigeration problem. Your approach of using the COP equation and determining the mass flow rate of water is correct.

To complete the problem, you are correct in using an energy balance equation. This will help you determine the power of the compressor needed for the refrigeration system. The energy balance equation is:

Qh = Win + Ql

Where Qh is the heat absorbed by the refrigerant in the evaporator, Win is the work input to the compressor, and Ql is the heat rejected by the refrigerant in the condenser.

To solve for the power of the compressor (Win), you can rearrange the COP equation as:

Win = Ql x (COP - 1)

Substituting the values given in the problem, we get:

Win = (0.00222 kg/s) x (2.9 - 1) x (22 C - 8 C)

Solving for Win, we get a power of approximately 0.014 W. This is the power required for the compressor to meet the cooling needs of the water fountain.

I hope this helps you complete your homework assignment. Remember to always use the appropriate equations and units when solving thermodynamics problems. Best of luck!