Question

For one mole of an ideal gas, three isochors were obtained at \(V_1, V_2\) and \(V_3\) respectively. Their slopes are \(m_1, m_2\) and \(m_3\). If \(V_1<V_2<V_3\), then the correct relationship of slopes is:

• A. \(m_2<m_3<m_1\)
• B. \(m_1<m_2<m_3\)
• C. \(m_1>m_2>m_3\)
• D. \(m_1 = m_2 = m_3\)

Hint:

Slope of an isochoric curve for ideal gas is inversely proportional to volume.

Answer 1

The Correct Option is C

For an ideal gas, at constant volume (isochor), pressure \(P\) varies linearly with temperature \(T\): \[ P = \frac{nRT}{V} \] Slope of isochor in \(P\)-\(T\) graph is: \[ m = \frac{nR}{V} \] Given \(n\) and \(R\) constants, slope inversely proportional to volume \(V\). 
Since \(V_1<V_2<V_3\), \[ m_1 = \frac{nR}{V_1}>m_2 = \frac{nR}{V_2}>m_3 = \frac{nR}{V_3} \]