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Which of the following represents Gay Lu...

Which of the following represents Gay Lussac's law ?
I.`(P)/(T)=` constant
II. ` P _(1) T _(2) = P_(2) T _(1)`
III.` P _(1) V _(1) = P _(2) V _(2)`
Choose the correct option .

A

I,II and III

B

II and III

C

I and III

D

I and II

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The correct Answer is:
To determine which of the given options represents Gay-Lussac's law, let's analyze each option step by step. ### Step 1: Understand Gay-Lussac's Law Gay-Lussac's law states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. Mathematically, this can be expressed as: \[ P \propto T \] or \[ \frac{P}{T} = \text{constant} \] ### Step 2: Analyze Each Option 1. **Option I: \( \frac{P}{T} = \text{constant} \)** - This directly represents Gay-Lussac's law, as it indicates that the ratio of pressure to temperature remains constant. 2. **Option II: \( P_1 T_2 = P_2 T_1 \)** - This equation is a rearrangement of the relationship derived from Gay-Lussac's law. It implies that if the pressure and temperature of a gas change, their product remains constant, which is consistent with Gay-Lussac's law. 3. **Option III: \( P_1 V_1 = P_2 V_2 \)** - This equation represents Boyle's law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This does not represent Gay-Lussac's law. ### Step 3: Conclusion From the analysis: - **Option I** and **Option II** are correct representations of Gay-Lussac's law. - **Option III** is incorrect. Thus, the correct options are **I and II**. ### Final Answer The correct options that represent Gay-Lussac's law are **I and II**. ---
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