Notebook

Estimation of Absolute Zero by use of the Gas Laws¶

Theory:¶

Charles’ law states that for a constant amount of gas, the volume is proportional to the absolute temperature if the pressure remains constant. V α T for constant P A plot of volume versus Centigrade temperature intercepts the x-axis at -273 oC which suggests that the gas would occupy no volume at this temperature. This theoretical value is known as absolute zero, and is also known as 0 Kelvin.

Apparatus:¶

Heat the water using a Bunsen burner and stir regularly. Measure the length of the trapped air every 10 oC up to 80 oC. Plot a graph of the length of trapped air (y-axis) against temperature (x-axis).

Extrapolating from the gradient should give a value for the x-axis intercept

In [12]:

# Importing the necessary libraries
from matplotlib import pyplot as plt
import numpy as np
#from prettytable import PrettyTable

# Preparing the data to be computed and plotted
dt = np.array([
          
    [1.0, 0.15],
    [2.0, 0.29],
    [3.0, 0.38],
    [4.0, 0.50],
    [5.0, 0.60],
    [6.0, 0.81],
    [7.0, 0.90],
    [8.0, 1.13]
])

# Preparing X and y data from the given data
x = dt[:, 0].reshape(dt.shape[0], 1)
X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)
y = dt[:, 1].reshape(dt.shape[0], 1)

# Calculating the parameters using the least square method
theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)

print(f'The parameters of the line: {theta}')

# Now, calculating the y-axis values against x-values according to
# the parameters theta0 and theta1
y_line = X.dot(theta)

# Plotting the data points and the best fit line
plt.scatter(x, y)
plt.plot(x, y_line, 'r')
plt.title('Best fit line using regression method')
plt.xlabel('Length in cm')
plt.ylabel('Resistance')

plt.show()



#def makePrettyTable(table_col1, table_col2):
 #   table = PrettyTable()
  #  table.add_column("Column-1", x)
   # table.add_column("Column-2", Y)
    #return table

The parameters of the line: [[ 0.13452381]
 [-0.01035714]]

Conclusion¶

In comparison, our calculated resistivity is 0.13 Ohm/m vs a databook value of 0.105 Ohm/m This is well within the expected variance of an A-level practical.

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