To solve for the final pressure [tex]\( P_2 \)[/tex] using the combined gas law, we start with the given equation:
[tex]\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\][/tex]
We need to rearrange this equation to solve for [tex]\( P_2 \)[/tex]. Let's look at the steps involved:
1. Isolate [tex]\( P_2 \)[/tex] on one side of the equation:
[tex]\[
P_2 = \frac{(P_1 V_1 / T_1) \times T_2}{V_2}
\][/tex]
2. Simplify the expression:
[tex]\[
P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}
\][/tex]
Here we can identify the Numerator (A) and Denominator (B) in the fraction:
- Numerator [tex]\( (A) \)[/tex] :
[tex]\[
P_1 V_1 T_2
\][/tex]
- Denominator [tex]\( (B) \)[/tex] :
[tex]\[
T_1 V_2
\][/tex]
So, when we rearrange the gas law to solve for [tex]\( P_2 \)[/tex], the variables in the numerator [tex]\( (A) \)[/tex] and denominator [tex]\( (B) \)[/tex] are:
- Numerator [tex]\( (A) \)[/tex] :
[tex]\[
P_1 V_1 T_2
\][/tex]
- Denominator [tex]\( (B) \)[/tex] :
[tex]\[
T_1 V_2
\][/tex]
These values correspond to each given option for numerator and denominator provided in the question.
