Physics: Agas is equilibrium at t kelvin. if mass of one molecule is m and its component of velocity in x direction is v. then mean of its v2 is 3kt 2kt 2 kt 3 (4) zero

Agas is equilibrium at t kelvin. if mass of one

Senica

11.03.2022

The value of $v_{x}^2$ is $\dfrac{KT}{M}$ .

Explanation:

A gas is equilibrium at T kelvin.

Mass = M

We know that,

The average square of the velocity in the x,y and z direction are equal.

$\bar{v}_{x}^2=\bar{v}_{y}^{2}=\bar{v}_{z}^{2}$

$v_{rms}^2=v_{x}^{2}+v_{y}^{2}+v_{z}^{2}$

$v_{rms}^2=3v_{x}^2$

$v_{x}^{2}=\dfrac{v_{rms}^2}{3}$

Equation of ideal gas

PV=RT

$P=\dfrac{nKT}{V}$

Here, R = nK

We know that,

$\dfrac{nKT}{V}=\dfrac{nM}{3V}v_{rms}^2$

$v_{rms}^2=\dfrac{3KT}{M}$ ....(I)

Put the value of $v_{rms}^2$ in the equation (I)

$v_{x}^2=\dfrac{1}{3}\times\dfrac{3KT}{M}$

$v_{x}^2=\dfrac{KT}{M}$

Hence, The value of $v_{x}^2$ is $\dfrac{KT}{M}$ .

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kawaiiblurainbow

31.10.2021

Celsius (°C)

Kelvin (K)

Fahrenheit (°F)

Rankine (°R or °Ra)

Explanation:

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