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×30th Oct 2019 @ 3 min read

The equation of Boyle's law is *PV* = k.

Boyle's law is a gas law discovered by Robert Boyle. It states the pressure of a gas is inversely proportional to the volume of the gas at a constant temperature and for a fixed amount of the gas.

Let the pressure of a gas be *P* and the volume of the gas be *V*. Thus, the above statement can be mathematically written as follows:

Removing the proportionality,

Here *k* is a proportionality constant. Rearranging the above equation,

Therefore, we can conclude the product of pressure and volume remains constant.

Let a gas moves from condition 1 (*P*_{1}, *V*_{1}) to condition 2 (*P*_{2}, *V*_{2}) and the temperature and amount of the gas remains the same.

With the help of Boyle's law, we can establish the relationship between both conditions.

As per the law, *P*_{1}*V*_{1} = *k* and *P*_{2}*V*_{2} = *k*.

Combining both expressions,

The formula *P*_{1}*V*_{1} = *P*_{2}*V*_{2} is very useful to determine unknown pressure or volume if other variables are known.

An example will give a better understanding of it.

A hydrogen balloon of 0.50 L at a pressure of 101.325 kPa expands isothermally to a final pressure of 80.121 kPa. Determine the final volume?

Initially, *P*_{1} = 101.325 kPa and *V*_{1} = 0.50 L and the final volume (*P*_{2}) is 80.121 kPa.

According to the law,

Therefore, the final volume of the balloon is 0.63 L.

Boyle's law equation is not limited up to two conditions but can generalised to any number of conditions. Let consider a gas under *i* different conditions (*P*_{1}, *P*_{2}, *P*_{3} … *P _{i}* and

According to the law, the product of pressure and volume remains constant.

In a closed system, helium gas undergoes isothermal compression from stage 1 to an intermediate stage 2 and then to the final stage 3. The temperature of the gas is maintained at 30 °C. The pressure in stage 1 and stage 2 is 1.0 atm and 2.0 atm, and the volume in stage 1 and stage 3 is 20 cm^{3} and 5 cm^{3}. Determine the unknown volume in stage 2 and the unknown pressure in stage 3?

Using the law,

The volume in stage 2 is

The pressure in stage 3 is

Therefore, the unknown volume is 10 cm^{3} and the unknown pressure is 4.0 atm.

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