Name: Molar Specific Heat Capacities of Gases
Uploaded: 2019-07-19
Duration: 10 min 31 s
Description: Do all gases have the same molar heat capacities? Are there certain criteria for determining molar specific heat capacities of gases? Watch the video to find...

Question

A sample of helium and neon gases has a temperature of $300 K$ and pressure of $1.0 atm$ . The molar mass of helium is $4.0 g {mol}^{- 1}$ and that of neon is $20.2 g {mol}^{- 1}$ .

(a) Find the rms speed of the helium atoms and of the neon atoms.
(b) What is the average kinetic energy per atom of each gas?

Accepted Answer

(a) The RMS speed of an ideal gas is given by,
$V_{r m s} = \sqrt{\frac{3 R T}{M}}$ , where, $R = 8.314 J {mol}^{- 1} K^{- 1}$ is the universal gas constant, $M$ is the molecular mass of the gas and $T = 300 K$ is the temperature.

From the given values, we can calculate rms speed of,

(1) Helium,
$V_{r m s} = \sqrt{\frac{3 \times 8.314 \times 300}{4 \times 10^{- 3}}}$
$= \sqrt{1.875 \times 10^{6}}$
$= 1.38 \times 10^{3} m s^{- 1}$ .
(2) Neon,
$V_{r m s} = \sqrt{\frac{3 \times 8.314 \times 300}{20.2 \times 10^{- 3}}}$
$= \sqrt{3.75 \times 10^{5}}$
$= 613 m s^{- 1}$ .

(b) The average kinetic energy per atom for inert gases is given by,
$K E = \frac{3}{2} k T$ , where, $k = 1.388 \times 10^{- 23}$ is the Boltzmann's constant and $T$ is the temperature (in Kelvin).

It is clear that the kinetic energy is independent of atomic mass. Hence, the kinetic energy of helium and neon atoms is the same. It's value is,
$K E = \frac{3}{2} \times 1.388 \times 10^{- 23} \times 300$
$≃ 6.2 \times 10^{- 21} J$ .

Important Questions on Thermometry, Thermal Expansion and Kinetic Theory of Gases

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A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar mass of helium is 4.0 g mol-1 and that of neon is 20.2 g mol-1. (a) Find the rms speed of the helium atoms and of the neon atoms. (b) What is the average kinetic energy per atom of each gas?

Important Questions on Thermometry, Thermal Expansion and Kinetic Theory of Gases

Learn and Prepare for any exam you want !