Confused on a question about vapour refrigeration cycle

[influx]

Homework Statement

http://photouploads.com/images/ae1d2f.png

Homework Equations

N/A

The Attempt at a Solution

In the image linked above, I have copied and pasted 4 different slides. In the last slide, I am confused how they got the expression for T2 (the working out). I know that they did the following:

[T2-(30+50)]/[(30+100)-(30+50)] = (5.623-5.417)/(5.75-5.417)
(T2-80)/(130-80) = (5.623-5.417)/(5.75-5.417)
(T2-80)/ = 50(5.623-5.417)/(5.75-5.417)
T2 = 80+ 50(5.623-5.417)/(5.75-5.417)

However, for the first step of the working, I am confused why the left hand side of the equation is like it is. Why do we have:

[T2-(30+50)]/[(30+100)-(30+50)] = (5.623-5.417)/(5.75-5.417)

I mean in terms of the vapour compression cycle, why is it -80 at the top and then 130-80 at the bottom? I know they got these values by adding the superheat temperature values but I am confused. Essentially what I want to know is what does 30+50 represent and what does 30+100 represent? If we are looking for the temperature at T2 why do we add 50 and 100 to 30 rather than to -20?

Also for h2, I am assuming that the 1610.9 inside the brackets is a typo and is supposed to be 1610.5?

 

[KataKoniK]

Hello,

Thank you for bringing up your confusion regarding the working out for T2 in the given image. Let me try to explain the reasoning behind the equations used.

Firstly, in order to find the temperature at T2, we need to use the equation for the vapour compression cycle, which is:

COP = T1/(T1-T2)

Where COP is the coefficient of performance, T1 is the temperature at the evaporator inlet, and T2 is the temperature at the condenser outlet.

Now, in the given image, we are given the values for T1 and COP, and we are asked to find the value for T2. So, we rearrange the equation:

T2 = T1 - (T1/COP)

Now, let's look at the first slide in the image. We can see that the given values for T1 and COP are 5.75 and 5.623 respectively. So, substituting these values in the rearranged equation, we get:

T2 = 5.75 - (5.75/5.623)

T2 = 5.75 - 1.023

T2 = 4.727

This is the value for T2 given in the first slide. Now, let's come to the last slide, where we are asked to find the value for T2 using the values for T1 and COP given in the fourth slide.

In order to find the value for T2, we need to use the same equation:

T2 = T1 - (T1/COP)

However, in this case, we do not have the value for T1 given directly. We only have the value for T1+(30+50), which is equal to 130. So, we need to use the given value for T1+(30+50) to find the value for T1 and then use it in the equation to find T2.

So, let's use the given equation:

[T2-(30+50)]/[(30+100)-(30+50)] = (5.623-5.417)/(5.75-5.417)

We can see that the values in the numerator and denominator on the left hand side of the equation represent the difference between the temperature at the condenser outlet (T2) and the temperature at the evaporator inlet (T1+(30+50)). Similarly, the values in the numerator and denominator