To make [tex]\( P_2 \)[/tex] the subject of the equation [tex]\( P_1 V_1 = P_2 V_2 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
P_1 V_1 = P_2 V_2
\][/tex]
2. To isolate [tex]\( P_2 \)[/tex], divide both sides of the equation by [tex]\( V_2 \)[/tex]:
[tex]\[
\frac{P_1 V_1}{V_2} = \frac{P_2 V_2}{V_2}
\][/tex]
3. On the right side, the [tex]\( V_2 \)[/tex] terms cancel out:
[tex]\[
\frac{P_1 V_1}{V_2} = P_2
\][/tex]
4. Rewrite the equation with [tex]\( P_2 \)[/tex] as the subject:
[tex]\[
P_2 = \frac{P_1 V_1}{V_2}
\][/tex]
So, the expression for [tex]\( P_2 \)[/tex] is:
[tex]\[
P_2 = \frac{P_1 V_1}{V_2}
\][/tex]
