Exercises

Exercises#

First, we must create NumPy arrays to storage each of the three columns of data in the table.

import numpy as np

p = np.array([5020, 60370, 20110, 46940, 362160])
V = np.array([0.8, 0.2, 1.0, 0.6, 0.1])
T = np.array([200, 600, 1000, 1400, 1800])

Now we plot, \(p\) against \(T\).

import matplotlib.pyplot as plt

plt.plot(T, p, 'o')
plt.xlabel('$T$')
plt.ylabel('$p$')
plt.show()
../_images/e62526f1bca0f189aee6709045e7d9b9c7a75e47b0e96d5706ec9b7ee68c5bed.png

Then \(V\) against \(T\)

plt.plot(T, V, 'o')
plt.xlabel('$T$')
plt.ylabel('$V$')
plt.show()
../_images/d31d126e5c2575948234233126395f55a41537dc3525ac9250635e29cf9ff107.png

Finally, \(pV\) against \(T\).

plt.plot(T, p * V, 'o')
plt.xlabel('$T$')
plt.ylabel('$pV$')
plt.show()
../_images/0af9eb8c65d417af9da4147c4224a80dfc215a3325d364a440645a69aa417ade.png

There is a clear linear relationship between \(pV\) and \(T\), the ideal gas relation.

We can now calculate \(n\) for each data point by rearranging the ideal gas law to read,

\[ n = \frac{pV}{RT} \]

and we can use NumPy array to perform this mathematics.

from scipy.constants import R

n = p * V / (R * T)

print(n)

[2.41506889 2.42028069 2.41867706 2.41953615 2.41987978]

We can then find the mean \(n\) and standard error as follows,

mean = np.mean(n)
std_err = np.std(n) / len(n)

print(mean, std_err)

2.4186885144638026 0.00037708831485353504

Note that the len() function will return the number of items in a list as an int.