Question

For one of a gas, $\gamma $ is equal to 1.66, the gas will be:
(a)- Monatomic
(b)- Diatomic
(c)- Triatomic
(d)- Tetra atomic

Answer 1

Hint: The gamma ($\gamma $) is the ratio of heat capacity at constant pressure to the heat capacity at constant volume. Monatomic gas means there is only one atom, diatomic means there are two atoms, tri atomic means there are three atoms, tetra atomic means there are four atoms.

Complete answer:
There are many types of gases present in the atmosphere, based on the number of atoms in the molecules we can classify them as:
Monatomic gas means there is only one atom, diatomic means there are two atoms, tri atomic means there are three atoms, tetra atomic means there are four atoms.
For all the gases there is a specific value of $\gamma $. The gamma ($\gamma $) is the ratio of heat capacity at constant pressure to the heat capacity at constant volume. The heat capacity at constant pressure is denoted as ${{C}_{p}}$ and the heat capacity at constant volume is represented as ${{C}_{v}}$. We can write:
\[\gamma =\dfrac{{{C}_{p}}}{{{C}_{v}}}\]
The given value of $\gamma $ for gas is 1.66, when we convert this value into the fractional form then we get:
$1.66=\dfrac{5}{3}$
This value is obtained for monatomic gases, for monatomic gas, ${{C}_{P}}$ is 5/2 R and ${{C}_{v}}$ is 3/2 R. we can calculate:
$\gamma =\dfrac{{{C}_{p}}}{{{C}_{v}}}=\dfrac{(5/2)R}{(3/2)R}=\dfrac{5}{3}$
So, the given gas will be monatomic gas.

Therefore, the correct answer is an option (a)- Monatomic.

Note:
The value of $\gamma $ for a diatomic gas is 1.40 or $\dfrac{7}{5}$ because the value of ${{C}_{P}}$ is 7/2 R and ${{C}_{v}}$ is 5/2 R. The value of $\gamma $ for a triatomic gas is 1.30 or $\dfrac{9}{7}$ because the value of ${{C}_{P}}$ is 9/2 R and ${{C}_{v}}$ is 7/2 R.