Question

Which from following is true according to Gay-Lussac's law?

• A. $\frac{\text{V}}{\text{T}} = \text{constant}$ at constant pressure and for fixed mass of gas.
• B. $\frac{\text{P}}{\text{d}} = \text{constant}$ at constant temperature and fixed mass of gas.
• C. $\frac{\text{P}}{\text{T}} = \text{constant}$ at constant volume and fixed mass of gas.
• D. $\text{P} \times \text{V} = \text{constant}$ at constant temperature and for fixed mass of gas.

Hint:

Boyle: $PV=k$; Charles: $V/T=k$; Gay-Lussac: $P/T=k$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Gay-Lussac's Law states the relationship between pressure and temperature of a gas.
Step 2: Key Formula or Approach:
$\text{P} \propto \text{T}$ at constant Volume ($\text{V}$) and moles ($\text{n}$).
Step 3: Detailed Explanation:
- Option (A) represents Charles's Law ($\text{V}/ \text{T} = \text{constant}$).
- Option (D) represents Boyle's Law ($\text{P} \times \text{V} = \text{constant}$).
- Gay-Lussac's Law states that for a fixed amount of gas at constant volume, the pressure is directly proportional to the absolute temperature. This is written as $\text{P}/\text{T} = \text{constant}$.
Step 4: Final Answer:
$\frac{\text{P}}{\text{T}} = \text{constant}$ at constant volume and fixed mass of gas is true.