Question

A gas occupied 250 cm³ at pressure P. If the pressure increases by 400%, find the new volume of gas, temperature remaining constant.

Answer 1

Step-1: Understand the given conditions

• Temperature is constant.
• Volume of gas = $250{\mathrm{cm}}^3$
• Pressure of gas= $\mathrm{P}$
• Volume to be calculated when final pressure increases by 400% of initial pressure

Step-2: Calculate the pressure after 400% increase in the initial pressure

Initial pressure ${\mathrm{P}}_1$= $\mathrm{P}$

Increase in the initial pressure= $\frac{400}{100}\mathrm{P}$

Final pressure ${\mathrm{P}}_2$ = ${\mathrm{P}}_1+\frac{400}{100}{\mathrm{P}}_1$

${\mathrm{P}}_2=\mathrm{P}+\frac{400}{100}\mathrm{P}$

${\mathrm{P}}_2=\mathrm{P}+4\mathrm{P}=5\mathrm{P}$

${\mathrm{P}}_2=5\mathrm{P}$

Step-3: Apply Boyle's law equation to find out the volume at the given pressure calculated above i.e.; $5\mathrm{P}$

Boyle's' law: According to Boyle's law, at constant temperature, pressure is inversely proportional to volume for a given mass of the gas.
or PV= constant

Therefore, for two different conditions i.e. 1 and 2, Boyle's' law can be written as:
${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

• Let volume of gas at pressure $\mathrm{P}$= ${\mathrm{V}}_1$i.e.; $250{\mathrm{cm}}^3$
• Let pressure of gas at volume ${\mathrm{V}}_1$= ${\mathrm{P}}_1$i.e.; $\mathrm{P}$
• Let pressure of gas at volume ${\mathrm{V}}_2$= i.e.; ${\mathrm{P}}_2$ = $5\mathrm{P}$ (calculated in Step-2)
• Let volume of gas at pressure ${\mathrm{P}}_2$= ${\mathrm{V}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} \mathrm{P}\times 250=5\mathrm{P}\times {\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{\mathrm{P}\times 250}{5\mathrm{P}} \\ {\mathrm{V}}_2=\frac{250\mathrm{P}}{5\mathrm{P}}=50{\mathrm{cm}}^3 \end{gathered}$$

${\mathrm{V}}_2=50{\mathrm{cm}}^3$