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 3 of 4: Coefficients of performance

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COP = \dfrac{Q}{W}: \quad COP(\ce{NH3}) = \dfrac{21.3}{2.67} = 7.98,\quad COP(\ce{CHF2Cl}) = \dfrac{20.0}{4.88} = 4.10

Analysis

Dividing the absorbed heat by the compression work gives $COP(\ce{NH3}) = 7.98$ and $COP(\ce{CHF2Cl}) = 4.10$ : despite safety drawbacks, ammonia is thermodynamically the better refrigerant.