Question

which formula represents gay-lussac’s law?
\\(\frac{v_1}{t_1} = \frac{v_1}{t_2}\\)
\\(\frac{p_1}{t_1} = \frac{p_1}{t_2}\\)
\\(p_1v_1 = p_2v_2\\)
\\(p_1t_1 = p_2t_2\\)

Explanation:

Gay - Lussac's law states that for a given mass of a gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature. Mathematically, this can be expressed as $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ (where $P$ is pressure and $T$ is absolute temperature) when the volume is constant. The first option $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ is Charles's law (relating volume and temperature at constant pressure). The third option $P_1V_1 = P_2V_2$ is Boyle's law (relating pressure and volume at constant temperature). The fourth option $P_1T_1=P_2T_2$ is not a valid gas law formula. So the formula representing Gay - Lussac's law is $\frac{P_1}{T_1}=\frac{P_2}{T_2}$.

Answer:

$\boldsymbol{\frac{P_1}{T_1}=\frac{P_2}{T_2}}$ (the second option among the given choices, with the formula $\frac{P_1}{T_1}=\frac{P_2}{T_2}$)