Certainly! The combined gas law is a relation between the pressure, volume, and temperature of a fixed amount of gas. It combines Charles's Law, Boyle's Law, and Gay-Lussac's Law.
The combined gas law is mathematically represented by:
[tex]\[ \frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2} \][/tex]
where:
- [tex]\( P_1 \)[/tex] is the initial pressure
- [tex]\( V_1 \)[/tex] is the initial volume
- [tex]\( T_1 \)[/tex] is the initial temperature (in Kelvin)
- [tex]\( P_2 \)[/tex] is the final pressure
- [tex]\( V_2 \)[/tex] is the final volume
- [tex]\( T_2 \)[/tex] is the final temperature (in Kelvin)
Now, let's evaluate the given options to check which one correctly matches this formula:
1. [tex]\( \frac{P_1 V_1}{V_1 V_2} \)[/tex]
- This expression is not in the format of the combined gas law.
2. [tex]\( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)[/tex]
- This expression matches exactly with the combined gas law.
3. [tex]\( P_1 V_1 - P_2 V_2 \)[/tex]
- This expression represents a difference between product terms, which is not correct.
Therefore, among the given options, the correct representation of the combined gas law is:
[tex]\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \][/tex]
which is the second option in your list. Since the question specifically asked to identify which equation represents the combined gas law and by the process of elimination, we conclude that the correct option is indeed:
[tex]\[ \boxed{2} \][/tex]
