# 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