Problem 1

New and well-forgotten old refrigerants. Refrigerants are compared thermodynamically in a model refrigeration cycle: liquid refrigerant boils at constant pressure

p_1

and temperature

T_1

(absorbing heat

Q

), the vapour is compressed reversibly and adiabatically to

T_2

(work

W

), then cooled at constant pressure

p_2

and returned to the initial state. For 1 mole of refrigerant with

T_1 = 280

K and

T_2 = 380

K, ideal vapour, the data are:

\ce{NH3}

—

\Delta H_{vap} = 21.3

kJ mol

^{-1}

C_V(\text{gas}) = 26.7

J K

^{-1}

mol

^{-1}

;

\ce{CHF2Cl}

—

20.0

kJ mol

^{-1}

and

48.8

J K

^{-1}

mol

^{-1}

;

\ce{CF3CH2F}

—

22.1

kJ mol

^{-1}

and

79

J K

^{-1}

mol

^{-1}

;

\ce{CF3CF=CH2}

—

19.1

kJ mol

^{-1}

and

120

J K

^{-1}

mol

^{-1}

. (a) Calculate

Q

and

W

for

\ce{NH3}

and

\ce{CHF2Cl}

. (b) The coefficient of performance is

COP = Q/W

; calculate it for both refrigerants. (c) Calculate the COP for

\ce{CF3CH2F}

and

\ce{CF3CF=CH2}

— did efficiency improve relative to

\ce{CHF2Cl}

Step 4 of 4: COP of third- and fourth-generation refrigerants

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COP(\ce{CF3CH2F}) = \dfrac{22.1}{79 \times 100 \times 10^{-3}} = 2.80,\quad COP(\ce{CF3CF=CH2}) = \dfrac{19.1}{120 \times 100 \times 10^{-3}} = 1.59 \Rightarrow \text{No}

Analysis

The same calculation gives $COP = 2.80$ for $\ce{CF3CH2F}$ and $1.59$ for $\ce{CF3CF=CH2}$ — both below 4.10, so the newer generations did not improve energy efficiency versus $\ce{CHF2Cl}$ ; they were adopted for environmental (ozone, greenhouse) reasons instead.

Common pitfall. Use

C_V

in J K

^{-1}

mol

^{-1}

and convert to kJ: forgetting the factor

10^{-3}

inflates

W

by 1000 and destroys the COP.