Learner Resource 3 - Boltzmann factor
calculations
Use these formulae to solve the following problems.
Boltzmann factor, fB =exp(- E / kT)
T = - E / ( k x ln fB )
k = 1.4 x10-23 JK-1
1. Calculate the Boltzmann factor for a system with an energy spacing of 10-20 J at a
temperature of 273 K.
2. Calculate the temperature at which a system with an energy spacing of 10-20 J has a
Boltzmann factor of 0.1.
3. The data in the table below was collected by students measuring the speed at which a jar
of syrup rolled down a slope when heated to different temperatures.
T/K
speed/ ms-1
293
0.0082
303
0.0070
308
0.014
313
0.040
318
0.051
323
0.056
328
0.093
1 / T K-1
Ln speed
(You might find it more convenient to do these tasks on a spreadsheet)
Complete the table by calculating the inverse of the absolute temperatures and the natural logs of
the speeds.
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Plot a graph of the data and determine the gradient of the line of best fit.
The gradient of the line is equal to - E / k. Multiply the value of your gradient by - k to determine the
value for E
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