Question

If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?

Short answer

If the volume of a gas is tripled at the same temperature and amount of gas, the pressure is reduced by three times.

Step-by-step solution

Definition of volume

The volume of a material is the quantity of space it occupies, whereas the mass is the amount of matter it contains.

Using Boyle’s Law to understand pressure-volume relationship

Boyle's law describes the relationship between a gas's pressure and volume at a constant temperature and mass.

According to this formula, absolute pressure is inversely proportional to volume.

\(\begin{aligned}{}P \propto \frac{1}{V}\\{\rm{PV = constant }}\\{{\rm{P}}_{\rm{1}}}{{\rm{V}}_{\rm{1}}}{\rm{ = constant ,}}\\{{\rm{P}}_{\rm{2}}}{{\rm{V}}_{\rm{2}}}{\rm{ = constant}}\end{aligned}\)

Therefore, \({P_1}{V_1} = {P_2}{V_2}\).

Solving given problem using above steps  

It is given that volume is tripled at constant temperature and amount of gas. Hence

Initial Volume \(\left( {{V_1}} \right) = {\rm{V}}\,\,atm\). Final Pressure \(\left( {{P_2}} \right) = 3\;{\rm{V}}\,\,atm.\)

Initial Pressure \(\left( {{P_1}} \right) = {\rm{P}}K\) Final Pressure \(\left( {{P_2}} \right) = ?K\).

\(\begin{aligned}{}{P_1}{V_1} = {P_2}{V_2}\\({\rm{P}})({\rm{V}}) = \left( {{P_2}} \right)(3\;{\rm{V}})\\{P_2} = \frac{{({\rm{P}})({\rm{V}})}}{{3\;{\rm{V}}}}\\ = \frac{{\rm{P}}}{3}\end{aligned}\)

Hence the pressure is reduced to one-third of the original pressure when the volume of a gas is tripled at the same temperature and amount of gas.