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Unformatted text preview: Solution to Homework #1 Problem 1.2 a. The solution to this problem is approached as follow: since we are looking at the temperature range between 0°C to 10°C, we can tell that water will not be an appropriate thermometric fluid because a given volume can correspond to two different temperatures. This can be seen in the next plot. Thus, what we need is volume to be a monotone increasing function of temperature in this range. b. If the mercury thermometer has only been calibrated at 0 and 100°C, the graph of volume of 1g versus temperature is a straight line as follows: 0.99995 1 1.00005 1.0001 1.00015 1.0002 2 4 6 8 10 Vol of Water °C Water Thermometer y = 1E-05x + 0.0736 R² = 1 0.0734 0.0736 0.0738 0.074 0.0742 0.0744 0.0746 0.0748 0.075 20 40 60 80 100 120 Temperature (°C) Calibrated at 0 and 100 The equation of the line is approximately: 5 ˆ 0.0736 10 s V T T (slope = 0.000013421, intercept = 0.073556) (1) where T s represents the temperature read in the calibrated thermometer scale. Now, we can calculate the T s for each volume given in the problem statement. This is compared to the actual temperature (T), and the difference (error) is calculated. This difference is T s- T , which give us the error graph. The graph is shown below: c. When a fluid-filled thermometer is used to measure the change in temperature, what one really measures is the change in length of the fluid along the capillary tube. This change in length, mathematically can be shown to be: A V L (2) where ΔV is the change in volume and A is the area. Thus, to have a good thermometer one needs a large V and a small area A . The small area is provided by the capillary, but the change in volume can be written as follows: ˆ V V M T T (3) Thus, the bulb is needed to provide the large mass M because the changes of volume with respect to temperature are small. Therefore, the right thermometer is one that has a capillary tube (small...
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This note was uploaded on 08/31/2011 for the course CHE 3473 taught by Professor Staff during the Spring '08 term at Oklahoma State.
- Spring '08
- Chemical Engineering