Question

The RMS velocity of a gas at 0 degrees is 2 metre per second The RMS velocity of the same gas at 819 degree C

Answer 1

Given:

The RMS velocity of a gas at 0 degrees is 2 metre per second.

To find:

RMS velocity of the same gas at 819°C.

Calculation:

At 0°C ;

$v = \sqrt{ \dfrac{3RT}{m} }$

$= > v = \sqrt{ \dfrac{3R(0 + 273)}{m} }$

$= > v = \sqrt{ \dfrac{3R( 273)}{m} }$

$= > 2 = \sqrt{ \dfrac{3R( 273)}{m} }$

$= > 2 = \sqrt{ \dfrac{3R}{m} } \times \sqrt{273}$

$= > \sqrt{ \dfrac{3R}{m} } = \dfrac{2}{ \sqrt{273} }$

At 819°C ;

$v2 = \sqrt{ \dfrac{3RT}{m} }$

$= > v2 = \sqrt{ \dfrac{3R(819 + 273)}{m} }$

$= > v2 = \sqrt{ \dfrac{3R(1092)}{m} }$

$= > v2 = \sqrt{ \dfrac{3R}{m} } \times \sqrt{1092}$

$= > v2 = \dfrac{2}{ \sqrt{273} } \times \sqrt{1092}$

$= > \: v2 = \dfrac{2}{2}$

$= > \: v2 = 1 \: m {s}^{ - 1}$

So, final answer is:

$\boxed{ \sf{ \: v2 = 1 \: m {s}^{ - 1} }}$

Answer 2

Given:

The RMS velocity of a gas at 0 degrees is 2 metre per second

To find:

The RMS velocity of the same gas at 819 degree C

Solution:

The formula used to calculate the velocity  of a gas is,

$V_{rms}=\sqrt{\dfrac{3RT}{m}}$

From given, we have,

Case 1:

The RMS velocity of a gas at 0 degrees is 2 m/s

V²rms = 3RT/m

2² = 3 × (R/m) × (0 + 273)

4 = 819 × (R/m)

R/m = 4/819

∴ R/m = 4.884004884 × 10^{-3}

Case 2:

The RMS velocity of a gas at 819 degrees is given as,

V²rms = 3RT/m

V²rms = 3 × (R/m) × (819 + 273)

V²rms = 3 × 4.884004884 × 10^{-3} × (1092)

V²rms = 16

Vrms = 4 m/s

Therefore, the RMS velocity of the same gas at 819 degree C is 4 m/s