Question

The product of volume and pressure of a given mass of an enclosed gas is a constant quantity at some constant temperature. Is this statement true? Which physical gas law does the above statement represent?

Answer 1

The given statement is true and Boyle's law is represented in the above statement.

• This can be justified as follows:

Boyle's Law:

According to Boyle’s law, at constant temperature, volume of a given mass of gas is directly proportional to the pressure of the gas.

• This law was given by Robert Boyle in 1662.

Boyle's law equation can be written mathematically as $\mathrm{P}\propto \frac{1}{\mathrm{V}}$

• $\mathrm{P}=\mathrm{k}\frac{1}{\mathrm{V}}$
• where P= pressure of the gas and V= Volume of the gas at constant temperature.
• Also, on removing the sign of proportionality, a constant of proportionality is introduced
• where k= constant of proportionality
• Therefore, $\mathrm{PV}=\mathrm{k}$
• i.e.; for a given mass of a gas, the product of pressure and volume of the gas is constant at a given temperature.

Therefore, the given statement is true with respect to Boyle's law.