Question

The RMS velocity of CO2 at a temperature
"T” is x cm/sec.At what tempeature, the RMS
velocity of CO2 would be 4x​

Answer 1

Given:

The RMS velocity of CO2 at a temperature

"T” is x cm/sec.

To find:

Temperature at which RMS Velocity of CO2 is 4x.

Calculation:

Let the required temperature be t ;

In the 1st case:

$\sf{ \therefore \: \sqrt{ \dfrac{3RT}{m} } = x}$

In the 2nd case:

$\sf{ \therefore \: \sqrt{ \dfrac{3Rt}{m} } = 4x}$

Dividing the two Equations ;

$\sf{\therefore \: \sqrt{ \dfrac{t}{T} } = 4}$

$\sf{ = > \: \dfrac{t}{T} = {4}^{2} }$

$\sf{ = > \: \dfrac{t}{T} = 16 }$

$\sf{ = > \: t = 16T }$

So, final answer is :

$\boxed{ \large{ \red{ \sf{ \: t = 16T }}}}$