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Where PT, PC, Pρ are the uncertainties associated with the temperature, concentration and density, respectively. The values for the precision of the measurement were taken to be ± 1oC for the thermocouple and 0.5 kg/m3 for the density (manufacturers spec). Since the function relating temperature and density to concentration is unknown, the partial derivatives are calculated by fitting a line to a set of values which are obtained by holding one variable constant while determining the concentration as the other variable takes on values over a range. Plots illustrating this are shown in Figures C.1 and C.2. The slope of the best fit line was taken to be the partial derivatives in Equation C.1. From this calculation the uncertainty in the concentration of the glycol solution is calculated to be 0.5%. The effect of uncertainty in the concentration on the uncertainty in the specific heat over a range of temperatures was calculated two ways. The first paralleled the method used to determine the uncertainty in the concentration: computing a partial derivative of specific heat with respect to concentration off the slope of a line of best fit and multiplying this times the precision of the concentration. The plot used to determine the value for the partial derivative is shown in Figure C.3. The resulting uncertainty in the specific heat, ultimately based on the uncertainty in the temperature and density measurements is calculated to be ± 0.01 kJ/kg K. To verify this value, the specific heat corresponding to +0.5% and –0.5% of the estimated concentration was evaluated over a range of temperature (-20oC to +20oC). The difference between the values which (varied by 1%) was 0.02 kJ/kg K which verifies the results from the first approach. 55.4 55.2 55 54.8 54.6 54.4 54.2 54 53.8 14.0 15.0 16.0 17.0 18.0 19.0 20.0 Temperature (C) y = 0.3133x + 49.207 Figure C.1 Calculated concentration dependence on temperature with fixed density 66 Concentration (%)PDF Image | Comparison of R744 and R410A
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