Its volume will be 12-fold.
From the Ideal Gas formula we know that:
[tex]\frac{P_{1\text{ }}\cdot V_1}{T_1}=\frac{P_2\cdot V_2}{T_2}[/tex]
- P is the pressure os the gas.
- V is the volume of the gas.
- T is the temperature of the gas.
So, we can replace the hypothetical values to calculate the volume of the gas:
[tex]\begin{gathered} \frac{P_{1\text{ }}\cdot V_1}{T_1}=\frac{P_2\cdot V_2}{T_2} \\ \\ \frac{P_{1\text{ }}\cdot V_1}{T_1}=\frac{P_{1\cdot}\frac{1}{3}\cdot V_2}{T_1\cdot4} \\ V_1=\frac{P_{1\cdot}\frac{1}{3}\cdot V_2\cdot T_1}{P_{1\text{ }}\cdot T_1\cdot4} \\ V_1=\frac{_{}\frac{1}{3}\cdot V_2_{}}{_{}4} \\ V_1\cdot4\cdot3=V_2 \\ V_1\cdot12=V_2 \end{gathered}[/tex]
Finally, its volume will be 12-fold.
