In this lab you will use your knowledge of heat and energy to measure the Specific Heat c of two different metals. The two metal samples will be heated from the friction between the sample and a taut string, sliding over the sample.

If we put energy $Q$ into an object having mass $m$, we will raise its temperature by an amount $\Delta T$ as

where $c$ is the specific heat of the object.

In this experiment we will displace a string by a distance $x$ over the sample by applying a force $F$ to the string. This process will require expenditure of energy $Q$ which we assume goes into the sample thus raising its temperature.

One member of the group should click on the link below to start your group lab notebook. (You may be asked to log into your UChicago Google account if you are not already logged in.) Make sure to share the document with everyone in the group (click the “Share” button in the top right corner of the screen) so each member has access to the notebook after you leave lab. Choose one member of your group to be the designated record-keeper.

Figure 1.

The apparatus we will use is shown in Fig. 1. You have two metal samples, one is Al the other is Brass. Each sample has a thermistor embedded in it which can be used to record the temperature of the sample. You have a piece of thick, coarse string which you will slide back and forth over the sample to create friction. A known mass hangs over a pulley which we will assume is frictionless. The pulley is attached to a rotary encoder which allows the rotational motion of the pulley to be recorded, which allows you to determine the motion of the hanging mass. Finally there is a force sensor with a hook attached to it.

The thick string is used to lift a mass, $M = 200$ g. The string is placed on the pulley of a rotary encoder, the rotation of which enables us to measure the displacement of the string. The string will also slide around the metal sample in its spiral groove. We use a force sensor to pull the string and lift the mass. The friction between the string and the sample will heat the sample. Embedded in the sample is a thermistor, a temperature-sensitive resistor that will enable us to measure the temperature of the sample.

A LabQuest Mini interface attached to the computer simultaneously records the output of the rotary encoder, the resistance of the thermistor and the force applied to the force sensor.

• The rotary encoder should be plugged into Dig 1 of the LabQuest Mini (LQM) interface.
• The force sensor should be switched to the 50 N range, and plugged into the Ch 1 input of the LQM.
• The thermistor should be connected to Ch 2, using the special cable assembly, to provide temperature measurement.

How does the thermistor work?

The temperature will be determined by measuring the resistance of the thermistor embedded in each sample. The relation between resistance and temperature is given on the base holding the samples and is plotted in Fig. 2

Figure 2: Plot of temperature, $T$, as a function of resistance, $R$, for thermistor

The solid line in Fig. 2 is a least-squares fit of a second-order polynomial to the $T$ vs. $R$ data. The resulting formula is given by

$T = 61.03 ~{}^{\circ}\textrm{C} - (4.771 \times 10^{-3} ~{}^{\circ}\textrm{C}/\Omega)R + (1.176 \times 10^{-7} ~{}^{\circ}\textrm{C}/\Omega^2)R^2$.

(5)

This relation has already been entered into the Friction software to give the temperature readout.

The Logger Pro configuration file named Friction records the data from the sensors and allows you to create plots of different quantities. Each lab station has two samples, one aluminum and one brass, each mounted on a black base. Do not remove the samples from their bases, since the wires to the thermistor are easily broken. We have measured the mass of each sample for you as follows:

• Aluminum sample mass, $m_{Al} = 0.0218 \pm 0.0001$ kg
• Brass sample mass, $m_{Br} = 0.0606 \pm 0.0001$ kg

The force sensor is a strain gauge which provides a voltage proportional to force applied to the hook. It is necessary to provide information to the software, correlating the voltage to a known force. After calibration, the force may be read from the computer.

You should check the calibration of the force sensor as follows. Pull down the Experiment menu and select Calibrate LabQuest Mini: 1 Ch1: Dual Range Force. In the popup window you can enter known masses for two calibration points. Use zero mass for one calibration point and a known mass for the other.

Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to submit to Canvas, but make sure everyone's name is on the document!

When you get home, you will need to write up your summary and your conclusions. This should be a separate document, and it should be done individually (though you may talk your group members or ask questions). Include any data tables, plots, etc. from the your lab notebook as necessary in order to show how your data support your conclusions.