Let’s walk through Boyle's Law and examine the given options to determine the correct one.
Boyle's Law states that for a given amount of gas at a fixed temperature, the pressure of the gas is inversely proportional to its volume. This relationship can be expressed mathematically as:
[tex]\[ P \times V = \text{constant} \][/tex]
This means if the volume decreases, the pressure increases, provided the temperature remains constant. The various forms of Boyle's law can be represented as:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
or
[tex]\[ P = \text{constant} \times \frac{1}{V} \][/tex]
Now let's analyze the given options:
I. [tex]\( P_1 V_1 = P_2 V_2 \)[/tex]
- This is a correct representation of Boyle's law. It shows that the product of initial pressure and volume is equal to the product of final pressure and volume if temperature and the amount of gas remain constant.
II. [tex]\( P = \text{constant} \times \frac{1}{V} \)[/tex]
- This option also correctly represents Boyle's law, stating that pressure is inversely proportional to volume.
III. [tex]\( \frac{P_1}{P_2} = \frac{T_1}{T_2} \)[/tex]
- This is not correct in the context of Boyle's law. This expression seems to relate pressure and temperature, but Boyle's law does not deal with temperature changes. Instead, it keeps temperature constant while examining the relationship between pressure and volume.
Given this analysis, the correct option aligned with Boyle's law among the provided ones is:
[tex]\[ \boxed{\text{II. } P = \text{constant} \times \frac{1}{V}} \][/tex]
Thus, the correct option is II.
