Question

identifying charless law
which formula represents charless law?
\\(\frac{p_1}{t_1} = \frac{p_2}{t_2}\\)
\\(\frac{v_1}{t_1} = \frac{v_2}{t_2}\\)
\\(\frac{p_1v_1}{t_1} = \frac{p_2v_2}{t_2}\\)
\\(p_1v_1 = p_2v_2\\)

Explanation:

Step1: Recall Charles's Law

Charles's Law states that for a fixed amount of gas at constant pressure, the volume \( V \) is directly proportional to the absolute temperature \( T \). Mathematically, this is expressed as \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) (when pressure is constant).

Step2: Analyze Each Option

• First option: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \) relates pressure and temperature (Gay - Lussac's Law, at constant volume), not Charles's Law.
• Second option: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) matches the definition of Charles's Law (volume - temperature relationship at constant pressure).
• Third option: \( \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} \) is the Ideal Gas Law in combined form, not Charles's Law.
• Fourth option: \( P_1V_1 = P_2V_2 \) is Boyle's Law (pressure - volume relationship at constant temperature), not Charles's Law.

Answer:

\(\boldsymbol{\frac{V_1}{T_1}=\frac{V_2}{T_2}}\) (the second formula)