91影视

The equation for Einstein solid at low temperature is calculated as:

$U=N蔚e^{-\left(\frac{蔚}{kT}\right)}\text{............(1)}$

Here, $N$is number of oscillator, $蔚$is the amount of energy quanta, $k$is Boltzmann constant and $T$is temperature.

Heat capacity at constant volume is given as:

$C_v={\left(\frac{鈭�U}{鈭�T}\right)}_{N,V}$

Where, $U$is internal energy.

By substututing the value of $U$in the above equation, we get,

$$\begin{gathered} C_v=\frac{鈭�}{鈭�T}\left(N蔚e^{-\left(\frac{蔚}{kT}\right)}\right) \\ {C}_v=\frac{N{蔚}^2}{k{T}^2}{e}^{-\left(\frac{蔚}{kT}\right)} \end{gathered}$$

Consider the equation which gives the relation of the heat capacity as a function of temperature:

$C_v=\frac{N{蔚}^2}{k{T}^2}{e}^{-\left(\frac{蔚}{kT}\right)}$

Now, by considering the rest other factors as a constant, heat capacity as a function of temperature can be given as:

$C_v鈭�\frac{1}{T^2}{e}^{-\left(\frac{1}{T}\right)}$

Based on the above relation, the graph can be plotted as below:

The required expression is derived as $C_v=\frac{N{蔚}^2}{k{T}^2}{e}^{-\left(\frac{蔚}{kT}\right)}$and the graph showing the heat capacity as a function of temperature can be made as follows: