Question
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 quantity $$\delta = \frac{{\Delta V}}{{V\,\Delta T}}$$ varies with temperature as
A.
B.
C.
D.
Answer :
Solution :
We know that $$\frac{V}{T} = {\text{constant}}$$
$$\therefore \,\,\frac{{V + \Delta T}}{{T + \Delta V}} = \frac{V}{T}\,\,{\text{or }}\frac{{\Delta V}}{{V\,\Delta T}} = \frac{1}{T}$$
We know that $$\frac{V}{T} = {\text{constant}}$$
$$\therefore \,\,\frac{{V + \Delta T}}{{T + \Delta V}} = \frac{V}{T}\,\,{\text{or }}\frac{{\Delta V}}{{V\,\Delta T}} = \frac{1}{T}$$