For a rigid diatomic molecule, the universal gas constant R = n CP , where, CP is the molar specific heat at constant pressure and n is a number. Hence, n is equal to

Question

For a rigid diatomic molecule, the universal gas constant R = n CP , where, CP is the molar specific heat at constant pressure and n is a number. Hence, n is equal to (A) 0.2257 (B) 0.4 (C) 0.2857 (D) 0.3557

Tardigrade Admin · Accepted Answer

For rigid diatomic molecule (CP/CV)=(7/5) ∴ CV=(5/7)CP Also CP-CV=R CP-(5/7)CP=R (2/7)CP=R ∴ n=(2/7)=0.2857

Q. For a rigid diatomic molecule, the universal gas constant $R = n C_{P}$ , where, $C_{P}$ is the molar specific heat at constant pressure and $n$ is a number. Hence, $n$ is equal to

$0.2257$

$0.4$

$0.2857$

$0.3557$

For rigid diatomic molecule
$\frac{C _{P}}{C _{V}} = \frac{7}{5}$
$∴ C_{V} = \frac{5}{7} C_{P}$
Also $C_{P} - C_{V} = R$
$C_{P} - \frac{5}{7} C_{P} = R$
$\frac{2}{7} C_{P} = R$
$∴ n = \frac{2}{7} = 0.2857$

Q. For a rigid diatomic molecule, the universal gas constant R=nCP​ , where, CP​ is the molar specific heat at constant pressure and n is a number. Hence, n is equal to

0.2257

0.4

0.2857

0.3557