Question

which is a correct way of stating amontonss (gay-lussacs) law? select the correct answer below: $p = kt$ $\frac { p } { t } = k$ $\frac { p _ { 1 } } { t _ { 1 } } = \frac { p _ { 2 } } { t _ { 2 } }$ all of the above

Explanation:

Step1: Understand Amontons's (Gay - Lussac's) law

Amontons's (Gay - Lussac's) law states that for a given amount of gas at constant volume, the pressure \(P\) of the gas is directly proportional to its absolute temperature \(T\).

Step2: Analyze each option

• For \(P = kT\): This is the direct proportionality form. If \(k\) is a constant (for a fixed amount of gas at constant volume), it shows \(P\propto T\).
• For \(\frac{P}{T}=k\): Rearranging \(P = kT\) gives \(\frac{P}{T}=k\), which also represents the constant ratio of pressure to temperature.
• For \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\): If we consider two different states (1 and 2) of the same gas at constant volume, from \(\frac{P}{T}=k\), we can write \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\) (since \(k\) is the same for the same gas at constant volume in both states)

Since all the given equations \(P = kT\), \(\frac{P}{T}=k\) and \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\) are valid representations of Amontons's (Gay - Lussac's) law, the answer is all of the above.

Answer:

all of the above