Question 179: Thermodynamics & KTG

Question

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Accepted Answer

Given the same room temperature of 300 K for helium and argon, we are tasked with finding the ratio of their average kinetic energies per molecule.
Formula for Kinetic Energy per Molecule:
$ \mathrm{K.E.} = \frac{\mathrm{f}}{2} \mathrm{kT} $
In this equation:
$\mathrm{f}$ is the degrees of freedom, which is 3 for both helium (He) and argon (Ar) since they are monatomic gases.
$k$ is the Boltzmann constant.
$T$ is the temperature in Kelvin.
Kinetic Energy Comparison:
For both helium and argon, since $\mathrm{f} = 3$, the expression simplifies:
$ \frac{\mathrm{K} \cdot \mathrm{E}_{\mathrm{He}}}{\mathrm{K} \cdot \mathrm{E}_{\mathrm{Ar}}} = \frac{1}{1} $
Thus, the average kinetic energy per molecule for both gases is the same at the same temperature, leading to a ratio of:
$ 1:1 $
This result implies that despite their differences in molar masses (helium being 4 g/mol and argon 40 g/mol), the average kinetic energy per molecule remains equal at the same temperature.

Answer

1 : $ \sqrt{10} $

Answer

10 : 1

Answer

1 : 10

Answer

1 : 1

Thermodynamics & KTG

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Choose the correct answer: