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Confused on a question about vapour refrigeration cycle (Thermodynamics) Watch

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    In the image I've linked above, I have copied and pasted 4 different slides. In the last slide, I am confused how they got the expression for T2 (as in 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)

    Which then gives:

    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?
 
 
 
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