If one mole of a polyatomic gas has two vibrational modes and - is the ratio of molar specific heats for polyatomic gas- - -CpCv- then the value of - is -

Here, number of translational degree of freedom =3 number nbsp;of rotational degree of freedom nbsp;=3 and nbsp;number of vibrational degree of freedom ...

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Standard XII

Chemistry

Heat Capacity at Constant Pressure

If one mole o...

Question

If one mole of a polyatomic gas has two vibrational modes and $β$ is the ratio of molar specific heats for polyatomic gas. $β = \frac{C_{p}}{C_{v}}$ , then the value of $β$ is :

1.35

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1.02

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1.25

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1.2

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Solution

The correct option is D $1.2$
Here, number of translational degree of freedom $= 3$
number of rotational degree of freedom $= 3$
and number of vibrational degree of freedom $= 2 \times 2 = 4$

Therefore, total number of degree of freedom, $f = 3 + 3 + 4 = 10$
$β = \frac{C_{p}}{C_{v}} = 1 + \frac{2}{f} = 1 + \frac{2}{10}$
$β = \frac{12}{10} = 1.2$

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If one mole of a polyatomic gas has two vibrational modes and β is the ratio of molar specific heats for polyatomic gas. β=CpCv, then the value of β is :

The correct option is D 1.2Here, number of translational degree of freedom =3 number of rotational degree of freedom =3 and number of vibrational degree of freedom =2×2=4 Therefore, total number of degree of freedom, f=3+3+4=10 β=CpCv=1+2f=1+210 β=1210=1.2

If one mole of a polyatomic gas has two vibrational modes and $β$ is the ratio of molar specific heats for polyatomic gas. $β = \frac{C_{p}}{C_{v}}$ , then the value of $β$ is :