Question

If the pressure exerted on gas is increased by 4 times and temperature is increased by 9 times, what will be the change in volume occupied by the gas?

Answer 1

Hint: Use combined gas equation law.

Step 1:
Given data:

Initial Case: Final Case

$$\begin{gathered} {\mathrm{P}}_1=\mathrm{P}\left(\mathrm{Say}\right) \\ T1=T\left(Say\right) \\ V1=V\left(Say\right) \end{gathered}$$ $$\begin{gathered} \mathrm{P}2=4\mathrm{PI}=4\mathrm{P} \\ \mathrm{T}2=9\mathrm{T}1=9\mathrm{T} \\ \mathrm{V}2=? \end{gathered}$$

Therefore

$$\begin{gathered} \raisebox{1ex}{$P_1{V}_1$}\!\left/ \!\raisebox{-1ex}{$T_1$}\right.=P_2{V}_2/T_2 \\ PV/T=4P{V}_2/9T \\ V2=9V/4 \end{gathered}$$

Step 2:
Change in volume,
ΔV = 9V/4 – V = 5V/4

Final Answer:
If the pressure exerted on gas is increased by 4 times and temperature is increased by 9 times the change in the volume will be 5V/4.