• Assignment 09A - For Beginning Spreadsheet Users

• Assignment 09B - For Experienced Spreadsheet Users (and all currently in University Physics)

Assignment 09A - For Introductory Spreadsheet Users

After discussing some of the basic concepts of spreadsheet use we will create a spreadsheet in class that computes the average value and standard deviation of a set of N different measurements.  If the measurements are identified by the variables x₁, x₂, x₃, ... , x_N then the average value of these measurements is given by

and the standard deviation of the measurements is given by

Assignment 09B - For Experienced Spreadsheet Users (and all currently in University Physics)

The molar heat capacity, C, of a material is defined as the amount of heat required per mole of the material per unit temperature change to raise the temperature of the material. If you have encountered heat capacity (or specific heat) in an introductory chemistry or physics class you probably assumed that the heat capacity was constant for a given material. This is true of most materials at temperatures near room temperature. However, at very low temperatures the heat capacity of a material is not constant – it varies with temperature.

The heat capacity of a metal at very low temperatures can be described by a contribution from the electrons in the metal that is linear with temperature and a contribution from atomic vibrations that varies as the cube of the temperature. In other words, the following expression can be written for the heat capacity as a function of temperature:

where A and B are constants (depending on the material) that describe the strength of the electron contribution and atomic vibration contribution to the heat capacity respectively.

If the above equation is divided by temperature we have

Then a graph of the heat capacity divided by temperature (C/T) versus the square of the temperature (T²) would be a linear relationship with slope B and y-intercept A.

The data below represent experimental measurements of the heat capacity of Copper (Cu) as a function of temperature from 0.2 K (Kelvin) to 1.7 K. The units of the heat capacity are millijoules per mol per Kelvin, or  mJ/(mol K).