# 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/m |
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,

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
```