An ideal gas is initially at a temperature T and volume V. Its volume is increased by \(\Delta V\) due to an increase in temperature \(\Delta T\), pressure remaining constant. The quantity \(\delta = \frac{\Delta V}{\Delta T}\) varies with temperature as :
Answer & explanation
Correct answer: option 3
From ideal gas equation :
- PV = RT ... [for 1 mol]
- P\(\Delta\)V = R\(\Delta\)T
Dividing (2) by (1), we get :
\(\frac{\Delta V}{V} = \frac{\Delta T}{T}\)
\(\Rightarrow \frac{\Delta V}{V\Delta T} = \frac{1}{T} = \delta\) ... [given]
\(\Rightarrow \delta = \frac{1}{T}\)
So, the graph between \(\delta\) and T will be a rectangular hyperbola.