[tex]$P_2=\frac{P}{2}$[/tex]the final pressure is half of the initial volume by doubling the pressure at constant
Let us understand how an ideal gas behaves at a constant temperature. As we know, the ideal gas law is defined by the following expression
PV=nRT
where n is the number of moles, R is the universal gas constant. For a gas, R and n are constant, so at constant T, the pressure is inversely proportional to volume as:
[tex]$\begin{aligned}P V &=C \\P & \propto \frac{1}{V}\end{aligned}$[/tex]
Thus, if the pressure of an ideal gas increases, the volume decreases and vice-versa.
Let;
- The initial pressure is [tex]$P_1=P$[/tex]
- The final pressure is [tex]$P_2[/tex]
- The initial volume is [tex]$V_1=V$[/tex]
- The final volume is [tex]V_2$=2V[/tex]
- The constant temperature is [tex]$T=T$[/tex]
According to the ideal gas law:
P V=n R T
At the constant n, R, and T, the ideal gas equation is;
[tex]$\begin{aligned}P V &=C \\P_1 V_1 &=P_2 V_2 \\P \times V &= P_2 \times2 V \\P_2 &=\frac{P}{2}\end{aligned}$[/tex]
Thus, [tex]$P_2=\frac{P}{2}$[/tex], the final volume is half of the initial volume by doubling the pressure at constant[tex]$\mathrm{T}$[/tex].
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