Investigation of the ideal gas law#

A large balloon is filled with argon gas, the temperature is then varied and the volume and pressure are measured. The results of this are shown in the table below.

Temperature/K

Volume/m3

Pressure/Pa

200

0.8

5020

600

0.2

60370

1000

1.0

20110

1400

0.6

46940

1800

0.1

362160

We will assume that the argon gas will follow the ideal gas law, which states,

\[ pV = nRT, \]

where, \(p\) is the pressure, \(V\) is the volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is the temperature. Carry out the following:

  • Plot the relationship between \(p\) and \(T\).

  • Plot the relationship between \(V\) and \(T\).

  • Plot the relationship between \(pV\) and \(T\).

  • For each data point calculate the value of \(n\), the number of moles of argon in the ballon, and store these values in a NumPy array.

  • Find the mean and standard error of this array (the standard error is the standard deviation divde by the [square root] of the sample size) and print these values in a string using the f-strings syntax.

Tip#

The ideal gas constant can be imported from the SciPy package and stored as the variable R with the following code:

from scipy.constants import R

Worked Example