import matplotlib.pyplot as plt
from numpy import linspace, exp

T = linspace(0.1, 300, 10000)

def Cv(T, k=1.38e-23, eps=1e-21):
    return ( (3*eps**2*exp(-eps/(k*T))) / ((3*exp(-eps/(k*T)) + 1)**2*k*T**2) )

plt.plot(T, Cv(T, eps=1e-21), label="$\epsilon = 1\cdot 10^{-21}$")
plt.plot(T, Cv(T, eps=2e-21), label="$\epsilon = 2\cdot 10^{-21}$")
plt.plot(T, Cv(T, eps=4e-21), label="$\epsilon = 4\cdot 10^{-21}$")
plt.legend()
plt.xlabel("Temperature $[K]$")
plt.ylabel("Heat capacity $C_V$")
plt.savefig("taskc.pdf")

29497371e5c88324d7838e4e3ca6d99c50e5dcac
<mask token>


def Cv(T, k=1.38e-23, eps=1e-21):
    return 3 * eps ** 2 * exp(-eps / (k * T)) / ((3 * exp(-eps / (k * T)) +
        1) ** 2 * k * T ** 2)


<mask token>

<mask token>


def Cv(T, k=1.38e-23, eps=1e-21):
    return 3 * eps ** 2 * exp(-eps / (k * T)) / ((3 * exp(-eps / (k * T)) +
        1) ** 2 * k * T ** 2)


plt.plot(T, Cv(T, eps=1e-21), label='$\\epsilon = 1\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=2e-21), label='$\\epsilon = 2\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=4e-21), label='$\\epsilon = 4\\cdot 10^{-21}$')
plt.legend()
plt.xlabel('Temperature $[K]$')
plt.ylabel('Heat capacity $C_V$')
plt.savefig('taskc.pdf')

<mask token>
T = linspace(0.1, 300, 10000)


def Cv(T, k=1.38e-23, eps=1e-21):
    return 3 * eps ** 2 * exp(-eps / (k * T)) / ((3 * exp(-eps / (k * T)) +
        1) ** 2 * k * T ** 2)


plt.plot(T, Cv(T, eps=1e-21), label='$\\epsilon = 1\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=2e-21), label='$\\epsilon = 2\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=4e-21), label='$\\epsilon = 4\\cdot 10^{-21}$')
plt.legend()
plt.xlabel('Temperature $[K]$')
plt.ylabel('Heat capacity $C_V$')
plt.savefig('taskc.pdf')

import matplotlib.pyplot as plt
from numpy import linspace, exp
T = linspace(0.1, 300, 10000)


def Cv(T, k=1.38e-23, eps=1e-21):
    return 3 * eps ** 2 * exp(-eps / (k * T)) / ((3 * exp(-eps / (k * T)) +
        1) ** 2 * k * T ** 2)


plt.plot(T, Cv(T, eps=1e-21), label='$\\epsilon = 1\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=2e-21), label='$\\epsilon = 2\\cdot 10^{-21}$')
plt.plot(T, Cv(T, eps=4e-21), label='$\\epsilon = 4\\cdot 10^{-21}$')
plt.legend()
plt.xlabel('Temperature $[K]$')
plt.ylabel('Heat capacity $C_V$')
plt.savefig('taskc.pdf')

import matplotlib.pyplot as plt
from numpy import linspace, exp

T = linspace(0.1, 300, 10000)

def Cv(T, k=1.38e-23, eps=1e-21):
    return ( (3*eps**2*exp(-eps/(k*T))) / ((3*exp(-eps/(k*T)) + 1)**2*k*T**2) )

plt.plot(T, Cv(T, eps=1e-21), label="$\epsilon = 1\cdot 10^{-21}$")
plt.plot(T, Cv(T, eps=2e-21), label="$\epsilon = 2\cdot 10^{-21}$")
plt.plot(T, Cv(T, eps=4e-21), label="$\epsilon = 4\cdot 10^{-21}$")
plt.legend()
plt.xlabel("Temperature $[K]$")
plt.ylabel("Heat capacity $C_V$")
plt.savefig("taskc.pdf")
