Estimate the partition function for the hypothetical

Step 1 of 3

Figure 6.3 is given as,

From figure 6.3, it is clear that the remaining energy states contribute in proportion to their Boltzmann factors, which are represented by the height of the bars in the graph. The total height of the nine bars, as measured by the ruler or scale, is approximately 13.0 cm , and the height of the first bar in the graph is approximately 4.4 cm. The ratio of the total height of the nine bars to the height of the first bar gives the partition function for the hypothetical system. So, the partition function for the hypothetical system is,

\(Z = 13/4.4\)

\(Z = 2.9545\)

Therefore, the partition function for the hypothetical system after rounding off to one significant figure is 3.

The ground state energy of the system is zero, so the exponential function \({e^{ - E\left( s \right)/kT}}\) becomes as follows,

\({e^{ - E\left( s \right)/kT}} = {e^0} = 1\)