(Solved): 15 Blood glucose sensor. To sense the concentration of glucose in blood for the purpose of monitor ...

15 Blood glucose sensor. To sense the concentration of glucose in blood for the purpose of monitoring diabetes, one can use a thermistor coated with the enzyme glucose oxidase and sense the temperature of the thermistor. Normal glucose levels in blood are between \( 3.6 \) and \( 5.8 \mathrm{mmol} / \mathrm{L} \). Glucose has the formula \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \) and has an enthalpy of \( 1270 \mathrm{~kJ} / \mathrm{mol} \). The thermistor has a heat capacity of \( 24 \mathrm{~mJ} / \mathrm{K} \) (the heat capacity for thermistors is typically given in \( \mathrm{mJ} / \mathrm{K} \), a quantity that takes into account its mass) and a nominal resistance of \( 24 \mathrm{k} \Omega \) at \( 20^{\circ} \mathrm{C} \). Assume the enzyme samples \( 0.1 \mathrm{mg} \) of blood. Assume as well that blood is mostly water. The sensing is done at the normal blood temperature of \( 36.8^{\circ} \mathrm{C} \). a. Calculate the increase in temperature of the thermistor over the range of normal glucose levels in blood. b. Calculate the sensitivity of the sensor over the span given. c. If, in addition, one measures the resistance of the thermistor as \( 18.68 \mathrm{k} \Omega \) at \( 30^{\circ} \mathrm{C} \), calculate the range and span of the resistance of the thermistor and its sensitivity in terms of the resistance measured.