Question

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 $\delta =\Delta V/V\Delta T$ varies with temperature as

• A. $\delta \propto T^2$
  
• B. $\delta \propto T$
  
• C. $\delta \propto \frac{1}{T}$
  
• D. $\delta \propto \sqrt{T}$
  

Answer 1

The correct option is C $\delta \propto \frac{1}{T}$

Ideal gas equation : $PV=nRT$

$⟹$ $V=\frac{nRT}{P}$ ..........(1)

Now the volume of gas is increased with increase in temperature keeping the pressure constant.

$\therefore$ $\Delta V=\frac{nR\Delta T}{P}$ $(\because P=constant)$ ...............(2)

Dividing (1) and (2) we get $\frac{\Delta V}{V}=\frac{\Delta T}{T}$

$\therefore$ $\delta =\frac{\Delta V}{V\Delta T}=\frac{1}{T}$

Thus the quantity $\delta$ is inversely proportional to temperature.