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Question 5.2.2: Calculating the Coefficient of Performance of an Automobile ...

Calculating the Coefficient of Performance of an Automobile Air Conditioner

An automobile air conditioner uses a vapor-compression refrigeration cycle with the environmentally friendly refrigerant HFC-134a as the working fluid. The following data are available for this cycle.

\begin{array}{clc}\hline \text { Point } & \text { Fluid State } & \text { Temperature } \\\hline 1 & \text { Saturated liquid } & 55^{\circ} C \\2 & \text { Vapor-liquid mixture } & \\3 & \text { Saturated vapor } & 5^{\circ} C \\4 & \text { Superheated vapor } & \\\hline\end{array}

a. Supply the missing temperatures and the pressures in the table.

b. Evaluate the coefficient of performance for the refrigeration cycle described in this problem.

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The keys to being able to solve this problem are (1) to identify the paths between the various locations and (2) to be able to use the thermodynamic properties chart of Fig. 3.3-4 for HFC-134a to obtain the properties at each of the locations. The following figure shows the path followed in the cycle, and the table provides the thermodynamic properties for each stage of the cycle as read from the figure.

With this information, the C.O.P. is

\text { C.O.P. }=\frac{\dot{Q}_{ B }}{\dot{W}}=\frac{\hat{H}_{3}-\hat{H}_{2}}{\hat{H}_{4}-\hat{H}_{3}}=\frac{402-280}{432-402}=4.07

[Since an equation of state specific to HFC-134a is not available, the Peng-Robinson equation (See Chapter 6) will be used. To proceed, we need to know the equilibrium pressures for HFC-134a as predicted by the Peng-Robinson equation of state. To calculate these use Analysis > Pure, and choose PL as the property we find at 5°C the vapor pressure is 3.484 bar = 0.3484 MPa and at 55°C the vapor pressure is 14.96 bar = 1.496 MPa. Using these results in the simulation, the following is obtained

\begin{array}{llllrr}\text { Point } & & T\left({ }^{\circ} C \right) & P( MPa ) & Q \text { (Watts) } & W \text { (Watts) } \\1 & \text { Condenser } & 55 & 1.496 & -152.84 & \\2 & \text { Valve } & 5 & 0.348 & & \\3 & \text { Boiler } & 5 & 0.348 & +122.31 & \\4 & \text { Pump } & 58.9 & 1.496 & & 30.53\end{array}

(Results for Q and W based on 1kg/sec flow.) The coefficient of performance is

\text { C.O.P }=\frac{122.31}{30.53}=4.01

in good agreement with the hand calculation using the results of using the thermodynamic properties chart for HFC-134a.

Also an Aspen \text { Plus }{ }^{\circledR} simulation with the Peng-Robinson equation of state is available Wiley website for this book in the folder Aspen>Illustration 5.2-2.]

3.3.4

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