When heat is added to most materials, the average amplitude of the atoms' vibration within the material increases. This, in turn, increases the separation between the atoms causing the material to expand. If the temperature change, , is such that the material does not go through a phase change, then it can be shown that the change in the object's length, , is given by the equationwhere , is the initial length of the object before heat is added, and , is the linear expansion coefficient of the material. Accepted values of several common materials are given below in Table 1.
This effect, however, is not simply limited to materials whose temperature has increased. If energy is removed from the material then the object's temperature will decrease causing the object tocontract. The temperature change, , from Equation 1 is always found by subtracting the initial temperature of the object from the final temperature, or therefore, if < 0, will also be negative, indicating a length contraction.
From Equation 1, we see that , is not only dependent on , but also on the initial length of the object, . So, the longer the object, the greater change in its length.Although the phenomena of linear thermal expansion can be problematic when designing bridges, buildings, aircraft and spacecraft, it can be put to beneficial uses. For instance, household thermostats and bi-metallic strips make use of the property of linear expansion.
Accepted Linear Expansion Values of Common Materials
In our experiment today we will use a thermistor to measure the change in the rod's temperature. A thermistor is a small, inexpensive electronic device, which is commonly used to measure temperature. Since the thermistor is essentially a resistor made of a semiconducting material, anincrease in temperature rapidly decreases the resistance of the device. Unfortunately the relationship between the thermistor's temperature and resistance is not linear, but rather logarithmic, making it somewhat inconvenient to use. The graph to the left shows this logarithmic behavior. The temperature versus resistance plot of a typical thermistor is given. Notice that the equation that fits thisdata is T = -24 Ln(R) + 139.48, where R is in kW.
N.B.: this is a plot of a typical thermistor and does not represent the thermistor that you will be using today!
Equipment and setup
(Figure 1.) Thermal expansion apparatus
(Figure 2.) Thermistor
(Figure 3.) Steam generator
(Figure 4.) The meter sticks and vertical stands are located in the window-well at the front of the classroom(Figure 5.) Two squirt bottles
(Figure 6.) Funnel and holder
(Figure 7.) Water runoff collection pan
(Figure 8.) Dial caliper
(Figure 9.) Digital multi-meter (DMM)
(Figure 10.) Hand protectors
Three metal rods (Al, Cu, and steel)
Two riser blocks
Hot water from sink
Caution!!! Rods may be very hot when using the steam generator! Use the hand protectors to remove hot rods.
Get your TA to check your steam generator between uses. If the water level is not at the proper level, you will experience time consuming problems.
Think before you start! You will be using a large amount of water throughout this lab; make sure your setup allows the water to flowsmoothly and that you have a continuous supply of water available!
You will be given a limited amount of ice. Your experiment should be designed so that the ice lasts for the duration of that day's experiment.
Note that the thermistor takes longer to reach thermal equilibrium than does the rod, so you must allow a fair amount of time (1-2 minutes) for the temperature measurement to stabilize....