Match the C p C v ratio for ideal gases with different type of molecules: Molecule Type C p / C v (A) Monoatomic (I) 7 / 5 (B) Diatomic rigid molecules (II) 9 / 7 (C) Diatomic non-rigid molecules (III) 4 / 3 (D) Triatomic rigid molecules (IV) 5 / 3

Question

Aicharya · Accepted Answer

Relation between the ratio of specific heat and degree of freedom is given by,

$γ = 1 + \frac{2}{f} . . . (1)$

For monoatomic molecule, $A$ , $f = 3$

$\Rightarrow γ = 1 + \frac{2}{3} = \frac{5}{3}$

For diatomic rigid molecule $B$ , $f = 5$

$\Rightarrow γ = 1 + \frac{2}{5} = \frac{7}{5}$

For diatomic non-rigid molecule $C$ , $f = 7$ $\Rightarrow γ = 1 + \frac{2}{7} = \frac{9}{7}$

For Triatomic rigid molecule $D$ , $f = 6$ $\Rightarrow γ = 1 + \frac{2}{6} = \frac{4}{3}$

Match the C p C v ratio for ideal gases with different type of molecules: Molecule Type C p / C v (A)…

Solution

Molecule Type	$C_{p} / C_{v}$
(A) Monoatomic	(I) $7 / 5$
(B) Diatomic rigid molecules	(II) $9 / 7$
(C) Diatomic non-rigid molecules	(III) $4 / 3$
(D) Triatomic rigid molecules	(IV) $5 / 3$