A triatomic molecule of an ideal gas is in the shape of a triangle. It can be assumed that the atoms are at the vertices of the triangle and joined by massless rods. Internal energy of $1 mole$ of the gas at temperature $T$ is $x R T$ . The value of $x$ is

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Solution

We know that, internal energy of an ideal gas is given by
$U = \frac{n f R T}{2}$
Here, number of moles $n = 1$

No. of degree of freedom $(f)$ = Total degrees of freedom $-$ Restricted degrees of freedom
$\Rightarrow$ $f = 3 N - 3$
where $N$ is the no. of atoms.

[Since there are translational, rotational & vibrational d.o.f for each atom. But the translational d.o.f are restricted by rigid rods joining them.]

$N = 3$ $($ For triatomic $)$
$\Rightarrow$ $f = 3 \times 3 - 3 = 6$

So, $U = \frac{1 \times 6 \times R T}{2}$
$\Rightarrow U = 3 R T$

Why this question?
Concept Involved - This question has been asked to test your memory for formulae of KTG and understanding of degrees of freedom of a molecule.

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