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×22nd Mar 2020 @ 3 min read

Boyle's law is a gas law. It dictates a pressure-volume relationship. The law states the pressure of an ideal gas is inversely proportional to its volume if the temperature and amount of the gas remain constant.

In other words, when the pressure of an ideal gas increases, its volume decreases, and vice versa. This is true as long as the temperature and amount of the gas remain constant.

Mathematically, we can express the law as:

or

Where, *P* is the absolute pressure of the gas, *V* is the volume, and *k* is a constant of proportionality.

Suppose an ideal gas is at the pressure *P*_{1} and volume *V*_{1}. Now, the gas undergoes expansion/contraction such that the temperature and amount of gas remain constant. After the change, the new pressure and volume of the gas are *P*_{2} and *V*_{2}.

Using the Boyle law, *P*_{1}*V*_{1} = *k* and *P*_{2}*V*_{2} = *k*. Thus, *P*_{1}*V*_{1} = *P*_{2}*V*_{2}. This expression is very useful to calculate unknown pressure or volume if the other three variables are known.

Let's take an example. The initial pressure and volume of an ideal gas are 1.0 atm and 1.0 m^{3}. The gas undergoes expansion, and its new volume is 2.0 m^{3}. Thus, *P*_{1}, *V*_{1}, and *V*_{2} are known to us. But, *P*_{2} is not known, which we can calculate as:

Therefore, the new pressure *P*_{2}, after the expansion, is 0.50 atm.

In the example, the volume changes from 1.0 m^{3} to 2.0 m^{3}, i.e., it doubles. As a consequence, the pressure changes from 1.0 atm to 0.50 atm, i.e., it halves. Thus, an increase in the volume causes the pressure to decrease. This is the Boyle law. When one increases, the other has to decrease, and vice versa.

Let's say, the same gas expands to *V*_{3} = 3 m^{3} instead of *V*_{2}. We can calculate the corresponding pressure *P*_{3} as:

Similarly, for every value of *V*, we can calculate the corresponding value of *P*. The table below lists volumes and its corresponding pressures.

P, atm | V, m^{3} |

1.0 | 1.0 |

0.50 | 2.0 |

0.33 | 3.0 |

0.25 | 4.0 |

0.20 | 5.0 |

0.17 | 6.0 |

0.14 | 7.0 |

We can plot the above data in a graph to get the graphical representation of Boyle's law. In the figure below, the pressure is on the *y*-axis, and the volume is on the *x*-axis. The curve in the graph is called the *PV* curve. It's an inverse proportional relationship—i.e., as the volume increases, the pressure decreases.

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