Refrigeration System Analysis

[cmmcnamara]

Homework Statement

Refrigeration system operates off Ref-134a. The refrigerant enters the compressor at 100kPa and -20C at a rate of 0.5 m^3/min, and leaves at 0.8MPa. The isentropic efficiency of the compressor is 78%. The refrigerant enters the throttling valve at 0.75MPa and 26C. It leaves the evaporator as a saturated vapor at -26C. Determine the power input of the compressor, the rate of heat removal from the refrigerated space, and the heat gain and pressure drop in the line between the evaporator and the compressor.

Neglect KE, PE and assume steady state operating conditions.

Homework Equations

All the usual thermodynamic relations

The Attempt at a Solution

This problem was pretty easy for the most part, just enthalpy calculations based on property table look up but my thinking isn't matching up on one part if I differ the thinking of problem solution.

From my own calculations I find the compressor input work to be 2.40 kW, the rate of heat loss from the line 0.202 kW. These answers are precisely those given in the book. My problem lies in the heat loss from the refrigerated space. I believe there are two ways to calculate this. One is first law across the evaporator which leads to the book answer which is 6.17kW. This is essentially the product of refrigerant flow rate with the change in enthalpy across the evaporator. However I think another way would be to do an energy balance across the entire system. This leads to 6.57 kW which is a difference of .40 kW to the result given by the book. I feel like these numbers should match up regardless of the method but I haven't been able to convince myself of where the error in my reasoning occurs. There are a few things I have mulled over:

-The process is the Rankine cycle with a mixture of ideal and non-ideal assumptions however the only assumption that is ideal that is used is that the throttling valve is isenthalpic. All the other states are specified in some manner or have ideal deviations
-I noticed the missing quantity is .40kW which is about double the line loss but I don't know if it is significant
-The only line loss specified is from evaporator to compressor, the other lines don't seem to have losses/gains I can identify


Can anyone help me identify what I am missing? I know there must be something because the energy balance method value for the entire system can't be a different value from that calculated from the constituent part the loss occurred across!

 

[KataKoniK]

Thank you for your post. It seems like you have put a lot of effort into finding the solution to this problem. However, I believe there may be a slight misunderstanding in your approach.

When calculating the rate of heat removal from the refrigerated space, it is important to consider the entire system, including the compressor and other components. This means that the energy balance should be done across the entire system, not just the evaporator.

In your attempt, you correctly calculated the compressor input work and the rate of heat loss from the line. However, the missing quantity of 0.40 kW is actually the rate of heat removal from the refrigerated space. This can be seen by doing an energy balance across the entire system, which would give you the same result.

I hope this helps clarify the issue. Keep up the good work in your studies!