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 of the gas is directly proportional to its absolute temperature. Mathematically, this is expressed as $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (where $V$ is volume and $T$ is absolute temperature), assuming pressure and amount of gas are 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, for constant volume), not Charles's Law.
• Second option: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ matches the formula for 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 option)