How the volume of the vessel, in which the ideal gas of constant mass is located

How the volume of the vessel, in which the ideal gas of constant mass is located, was changed, if its pressure was isothermally decreased by 5 times

Given:

V1 is the initial volume of the vessel in which the ideal gas of constant mass is located;

P2 = P1 / 5 – the gas pressure has decreased isothermally by 5 times.

It is required to determine V2 / V1 – how the volume of the vessel has changed.

Since, according to the condition of the problem, the process took place at a constant temperature (isothermal), then, in order to determine the change in volume, it is necessary to use the following formula:

P1 * V1 = P2 * V2;

V2 = P1 * V1 / P2;

V2 = P1 * V1 / (P1 / 5) = 5 * P1 * V1 / P1 = 5 * V1.

That is:

V2 / V1 = 5 * V1 / V1 = 5 times.

Answer: the volume of the vessel was increased 5 times.