Your physics teacher assigned a thermometer-building project. He gave you a glass tube with an inside diameter of 1.15 mm and a receptacle at one end. He also gave you 8.97 cm^3 of mercury to pour into the tube, which filled the receptacle and some of the tube. You are to add marks indicating degrees Celsius on the glass tube. At what increments should the marks be put on? You know the volume expansion coefficient of mercury is 1.82·10^-4°C^-1
Each 1 deg C change in temperature will increase the total volume by
dV = V*1.82·10^-4°C^-1 *1 °C = 0.00016 cm^3
That volume increase will increase the length in the cylindrical column by
dL = dV/(pi*R^2)= 3.9 cm for each 1 degree C change in temperature.
That number seems too high to me
3.9 cm it's not true :(
To determine the increments at which the marks should be put on the glass tube, we need to consider the volume expansion of mercury with temperature.
The volume expansion coefficient of mercury, given as 1.82·10^-4 °C^-1, tells us that for every degree Celsius increase in temperature, the volume of mercury expands by 1.82·10^-4 times.
First, let's find the initial volume of mercury in the glass tube. Given that 8.97 cm^3 of mercury filled the receptacle and some of the tube, we need to subtract the volume of the receptacle from the total volume to find out the amount of mercury in the tube.
Next, we need to determine the temperature range over which we want to measure with the thermometer. Let's assume we want to measure from 0°C to 100°C, a range of 100 degrees.
Now, we can calculate the total volume expansion of the mercury in the tube over this temperature range. Multiply the initial volume of mercury by the temperature range (in degrees Celsius) and then multiply it by the volume expansion coefficient:
Total volume expansion = Initial volume × Temperature range × Volume expansion coefficient
Divide the total volume expansion by the number of increments (marks) we want to put on the tube to find the volume expansion per increment.
To find the length increment for each mark on the tube, divide the volume expansion per increment by the cross-sectional area of the tube.
Finally, you can use the length increment to mark the tube at regular intervals, indicating the degrees Celsius.
Keep in mind that the accuracy and precision of the glass tube, markings, and measuring instrument will affect the reliability and readability of the resulting thermometer.