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, it can be expressed as $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ (where $V_1, V_2$ are volumes and $T_1, T_2$ are absolute temperatures), when pressure is constant.

Step2: Analyze each option

• First option: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ relates pressure and temperature, which is 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 mathematical form 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 Combined Gas Law, which combines Boyle's, Charles's, and Gay - Lussac's Laws.
• Fourth option: $P_1V_1 = P_2V_2$ is Boyle's Law (relates pressure and volume at constant temperature).

Answer:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$ (the second formula in the list)