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

The question involves understanding isotherms for an ideal gas. An isotherm is a curve that represents the relationship between pressure \(p\) and volume \(V\) at a constant temperature.

The ideal gas equation is given by:

\(pV = nRT\)

Where:

• \(p\) = Pressure
• \(V\) = Volume
• \(n\) = Number of moles of the gas
• \(R\) = Universal gas constant
• \(T\) = Temperature

Since the temperature is constant, the product \(pV\) is also constant along an isotherm. For two different masses \(m_1\) and \(m_2\) of a gas, the number of moles \(n\) changes. If \(m_1\) represents more moles than \(m_2\), then the curve for \(m_1\) will shift downwards due to higher volume or lower pressure for the same temperature.

Analyzing the diagram:

The isotherm for \(m_1\) lies below that of \(m_2\), indicating that the gas volume at a given pressure is larger for \(m_1\) or equivalently the pressure is lower for the same volume.

This implies \(m_1\) has more moles than \(m_2\), hence \(m_1 > m_2\).

Therefore, the correct option is: \(m_{1} > m_{2}\)