Question

At a particular temperature, a certain quantity of a gas occupies a volume of $74{\mathrm{cm}}^3$ at a pressure of$760\mathrm{mm}$. If the pressure is decreased to$740\mathrm{mm}$, what will be the volume of the gas at the same temperature?

Answer 1

The initial volume of gas$\left({\mathrm{V}}_1\right)=74{\mathrm{cm}}^3$; initial pressure of gas $\left({\mathrm{P}}_1\right)=760\mathrm{mm}$ at a constant temperature.

The final volume of gas$\left({\mathrm{V}}_2\right)=?$; final pressure of gas $\left({\mathrm{P}}_2\right)=740\mathrm{mm}$ at a constant temperature.

Since the temperature is constant, According to Boyle's law,

${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

Putting the values of pressure and volume

$\Rightarrow 760\mathrm{mm}\times 74{\mathrm{cm}}^3=740\mathrm{mm}\times {\mathrm{V}}_2$

$\Rightarrow \frac{760\mathrm{mm}\times 74{\mathrm{cm}}^3}{740\mathrm{mm}}={\mathrm{V}}_2$

Hence, ${\mathrm{V}}_2=76{\mathrm{cm}}^3$