question_answer

An ideal gas is initially at temperature T and volume V. Its volume is increased by \[\Delta V\] due to an increase in temperature \[\Delta T,\] pressure remaining constant. The physical quantity \[\delta =\frac{\Delta T}{V\Delta T}\] varies with temperature as

A)           

B)                  

C)

D)                                

Correct Answer: C

Solution :

                 From ideal gas equation                 \[pV=RT\]                 or            \[p\Delta V=R\Delta T\]                 Dividing eq. (ii) by eq. (i), we get                 \[\frac{\Delta V}{V}=\frac{\Delta T}{T}\]                 \[\frac{\Delta V}{V\Delta T}=\frac{1}{T}=\delta \]                 \[\therefore \] \[\delta =\frac{1}{T}.\] So, the graph between \[\delta \] and T will be rectangular graph.