Name: Difference Between Ideal Gas and Real Gas
Uploaded: 2019-07-19
Duration: 6 min 16 s
Description: What is real gas? What is the difference between real gas and ideal gas? Watch this video to learn about this interesting concept of real gases.

Question

The atmospheric density at an altitude $2500 km$ is about $1 \times 10^{6}$ molecules per $m^{3}$ .

$(A)$ Assuming the molecular diameter to be $2.0 \times 10^{- 8} cm$ , find the mean free path.

$(B)$ Explain whether the predicted value is meaningful.

Given:- Boltzmann constant( $k$ )= $1.38 \times 10^{- 23} J K^{- 1}$ .

Accepted Answer

The mean free path is the average distance travelled by a molecule between the successive collisions.

The mean free path for molecules in a gas is given by,

$λ = \frac{V}{\sqrt{2} π d^{2} N}$

where,

$2.0 \times 10^{- 8} cm$ is the diameter of a molecule

$N$ is the number of molecules in volume $V$

$(A)$ To get mean free path,

Substitute $d = 2.0 \times 10^{- 10} m$ and $\frac{N}{V} = 1 \times 10^{6}$ molecules per $m^{3}$ , we get,

$λ = \frac{1}{\sqrt{2} π {(2.0 \times 10^{- 10} m)}^{2} (1 \times 10^{6} m^{- 3})} = 6 \times 10^{12} m$

$(B)$

At this altitude, most of the gas particles are in an orbit around the Earth and do not suffer randomized collisions.

The mean free path has a little physical significance.

The mean free path is inversely proportional to the number density, $\frac{N}{V}$ .

The typical value of $\frac{N}{V}$ at room temperature, and, atmospheric pressure for an ideal gas at ground is,

$\frac{N}{V} = \frac{p}{k T} = \frac{1.01 \times 10^{5} Pa}{(1.38 \times 10^{- 23} J K^{- 1}) (298 K)} = 2.46 \times 10^{25} molecules m^{- 3} = 2.46 \times 10^{19} molecules {cm}^{- 3}$

This is much higher than that in the outer space so the mean free path will be much less and will have higher significance.

Important Questions on The Kinetic Theory of Gases

Learn and Prepare for any exam you want !

The atmospheric density at an altitude 2500 km is about 1×106 molecules per m3. A Assuming the molecular diameter to be 2.0×10-8 cm, find the mean free path. B Explain whether the predicted value is meaningful. Given:- Boltzmann constant(k)=1.38×10-23 J K-1.

Important Questions on The Kinetic Theory of Gases

Learn and Prepare for any exam you want !