Question

An ideal gas molecule is present at 27${}^{\circ }\text{C}$. By how many degree centigrade its temperature should be raised so that its ${\text{V}}_{\text{rms}}\text{,}{\text{V}}_{\text{mp}}\text{and}{\text{V}}_{\text{av}}$all may double?

• A. 900${}^{\circ }\text{C}$
• B. 108${}^{\circ }\text{C}$
• C. 927${}^{\circ }\text{C}$
• D. 81${}^{\circ }\text{C}$

Answer 1

The correct option is C 927${}^{\circ }\text{C}$

Solution:- (C) $927℃$

$T=27℃=(27+273)K=300K$

$V_{av}=\sqrt{\frac{8RT}{\pi M}}$

$\Rightarrow V_{av}\propto \sqrt{T}$

$V_{rms}=\sqrt{\frac{3RT}{M}}$

$\Rightarrow V_{rms}\propto \sqrt{T}$

$V_{mp}=\sqrt{\frac{2RT}{M}}$

$\Rightarrow V_{mp}\propto \sqrt{T}$

Thus to double the velocity, the temperature should be raised $4$ times.

Therefore,

$T^{\prime }=4T=4\times 300=1200K=927℃$

Hence the temperature should be raised to $927℃$.