The ideal gas equation is given as,
[tex]PV=RT[/tex]
Here, P is the pressure, V is the volume, R is universal gas constant and T is the temperature.
Let consider the initial case, when pressure is P1, volume is V1 and temperature is T1. The ideal gas equation is given as,
[tex]P_1V_1=RT_1\ldots(1)[/tex]
Consider the case, when pressure is P2, volume is V2 and temperature is T2. The ideal gas equatiojn is given as,
[tex]P_2V_2=RT_2\ldots(2)[/tex]
Dividing equation (1) by equation (2);
[tex]\frac{P_1V_1}{P_2V_2}=\frac{RT_1}{RT_2}[/tex]
Therefore,
[tex]\frac{V_1}{V_2}=\frac{T_1}{T_2}\times\frac{P_2}{P_1}[/tex]
Since,
[tex]P_2=2P_1[/tex]
And,
[tex]T_2=2T_1[/tex]
Therefore,
[tex]\begin{gathered} \frac{V_1}{V_2}=\frac{T_1}{2T_1}\times\frac{2P_1}{P_1} \\ \frac{V_1}{V_2}=1 \\ V_2=V_1 \end{gathered}[/tex]
Therefore, the final volume V2 is equal to initial volume V1. Hence, option (b) is the correct choice.
