Question

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature of the same ideal gas are shown for masses $m_{1}$ and $m_{2}$ of the gas respectively in the figure given, then}

• A. $m_{1}>m_{2}$
• B. $m_{1} = m_{2}$
• C. $m_{1}<m_{2}$
• D. $m_{1} \geq m_{2}$

Hint:

Higher isotherm means larger $pV$, hence larger mass at same temperature.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
From ideal gas equation $pV = nRT = \frac{m}{M}RT$.
Step 2: Detailed Explanation:
For a given $T$, $pV \propto m$. The curve with larger $pV$ product at the same $p$ or $V$ corresponds to larger mass. From the figure, the curve for $m_1$ has higher $pV$ product, so $m_1>m_2$.
Step 3: Final Answer:
$m_1>m_2$.