Question 2.15: A refrigeration process includes a compressor, as explained ...

A refrigeration process includes a compressor, as explained in detail in chapter 5, because it is necessary to change the boiling point of the refrigerant, which is done by controlling the pressure. Chapter 3 shows that the work required for compression is well approximated as equal to the change in enthalpy. Use Appendix F to find the change in specific enthalpy for each of the scenarios A-C:

A) Freon 22 enters the compressor as saturated vapor at P = 0.5 bar and exits the compressor at P = 2 bar and T = 20°C.
B) Freon 22 enters the compressor as saturated vapor at P = 2 bar and exits the compressor at P = 8 bar and T = 60°C.
C) Freon 22 enters the compressor as saturated vapor at P=5 bar and exits the compressor at P = 20 bar and T = 80°C.
D) In these three compressors, the inlet and outlet pressures varied considerably, but the “compression ratio” P_{\text {out }} / P_{i n} was always 4. What do you notice about the changes in enthalpy for the three cases?

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A) \Delta \widehat{\mathrm{H}}=\widehat{\mathrm{H}}_{\mathrm{out}}-\widehat{\mathrm{H}}_{\mathrm{in}}

Freon 22, saturated vapor and 0.5 bar \rightarrow 383 \frac{\mathrm{kJ}}{\mathrm{kg}}

Freon 22, 2 bar and 20^{\circ} \mathrm{C} \rightarrow 425 \frac{\mathrm{kJ}}{\mathrm{kg}}

425 \frac{\mathrm{kJ}}{\mathrm{kg}}-383 \frac{\mathrm{kJ}}{\mathrm{kg}}=\bf42 \frac{\mathbf{kJ}}{\mathbf{kg}}

B) Freon 22, saturated vapor and 2 bar \rightarrow 396 \frac{\mathrm{kJ}}{\mathrm{kg}}

Freon 22, 8 bar and 60^{\circ} \mathrm{C} \rightarrow 445 \frac{\mathrm{kJ}}{\mathrm{kg}}

445 \frac{\mathrm{kJ}}{\mathrm{kg}}-396 \frac{\mathrm{kJ}}{\mathrm{kg}}=\bf 49 \frac{\mathbf{k J}}{\mathbf{kg}}

C) Freon 22, saturated vapor and 5 bar \rightarrow 405 \frac{\mathrm{kJ}}{\mathrm{kg}}

Freon 22, 20 bar and 80^{\circ} \mathrm{C} \rightarrow 445 \frac{\mathrm{kJ}}{\mathrm{kg}}

445 \frac{\mathrm{kJ}}{\mathrm{kg}}-405 \frac{\mathrm{kJ}}{\mathrm{kg}}=40 \frac{\mathbf{k J}}{\mathrm{kg}}

D) The consistency in compression ratio (always 4) and consistency in \Delta \widehat{\mathrm{H}} (between 40 \frac{\mathrm{kJ}}{\mathrm{kg}} and \left.50 \frac{\mathrm{kJ}}{\mathrm{kg}}\right) leads us to believe that the compression ratio \left(P_{\text {out }} / P_{i n}\right) is a major factor influencing \Delta \widehat{\mathrm{H}} (for Freon 22 vapors). Indeed, in real compressors, the compression ratio is far more important than the absolute values of pressure in determining required work.

But you might wonder, why does the temperature change in a compressor, and are the particular combinations of inlet and outlet temperatures and pressures used in this problem realistic? These issues will be explored in Chapter 4, when we begin to discuss reversible processes and efficiencies.

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