Which equation represents the combined gas law?

A. [tex] P_1 V_1 = P_2 V_2 \]
B. [tex] \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
C. [tex] \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]



Answer :

Sure, let's determine which equation represents the combined gas law. The combined gas law is a relationship between pressure (P), volume (V), and temperature (T) of a gas. It combines three gas laws: Boyle's law, Charles's law, and Gay-Lussac's law. The combined gas law can be formulated as:

[tex]\[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \][/tex]

We will now analyze each given option to see which one matches this form:

1. \( P_1V_1 = P_2 V_2 \)
- This equation is incorrect because it doesn't include temperature (T1 and T2).

2. \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)
- This equation is in an incorrect format. It seems to mix volume and temperature but fails to include both pressures (P1 and P2).

3. \( P_1 \frac{P_2V_2}{T_2} \)
- This equation is also incorrect because it does not correctly structure the combined gas law and includes a misplaced term.

4. \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \)
- This equation is correct and accurately represents the combined gas law.

Thus, the correct equation representing the combined gas law is:

[tex]\[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \][/tex]

Therefore, the correct option is:

[tex]\[ 4 \][/tex]