Question

At what temperature the rms velocity of a gas shown at 50 degree centigrade will be doubled

Answer 1

RMS directly proportion to √T. so do double RMS temperature should be 4 times. T=4×(50+273)=4×323=1292 K or 1292-273=1019 degree Centigrade

Answer 2

Given:

• Temperature of gas = 50°C

To find:

• Temperature at which the RMS velocity of the gas will be doubled ?

Calculation:

The general expression for RMS velocity is:

$v_{RMS}=\sqrt{\dfrac{3RT}{M}}$

$\implies v_{RMS}=\sqrt{T}$

Now, initial temperature is 50°C = 50 + 273 = 323 K.

Now, we can say:

$\dfrac{v1_{RMS}}{v2_{RMS}} = \dfrac{ \sqrt{T1}}{\sqrt{T2}}$

$\implies \dfrac{v1_{RMS}}{2 \times (v1_{RMS})} = \dfrac{ \sqrt{323}}{\sqrt{T2}}$

$\implies \dfrac{1}{2 } = \dfrac{ \sqrt{323}}{\sqrt{T2}}$

$\implies T2 = 323 \times 4$

$\implies T2 = 1292 \: K$

So, temperature at which RMS velocity doubles is 1292 K.