For a gas Y -1-4- Then atomicity- C p and C V respectively of the gas areA- Monoatomic- 5 R -2- 3 R -2B- Monoatomic- 7 R -2- 5 R -2C- Diatomic- 7 R -2- 5 R -2- 2-2D- Triatomic- 7 R -2- 5 R -2

The correct option is C Diatomic, 7R2, 5R2Given: γ=1.4 C_p C_V=R ...(i) & γ =C_pC_V ⇒C_pC_V=1.4=75 substituting in Eq (i), 75C_V C_V=R ⇒25C_V=R Or, C_V=5R ...

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Standard XII

Physics

Heat Capacity

For a gas Y =...

Question

For a gas $γ = 1.4$ . Then atomicity, $C_{p}$ and $C_{V}$ respectively of the gas are

Monoatomic,

\frac{5 R}{2}, \frac{3 R}{2}

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Monoatomic,

\frac{7 R}{2}, \frac{5 R}{2}

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Diatomic,

\frac{7 R}{2}, \frac{5 R}{2}

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Triatomic,

\frac{7 R}{2}, \frac{5 R}{2}

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Solution

The correct option is C Diatomic, $\frac{7 R}{2}, \frac{5 R}{2}$
Given: $γ = 1.4$
$C_{p} - C_{V} = R . . . (i)$
$& γ = \frac{C_{p}}{C_{V}}$
$\Rightarrow \frac{C_{p}}{C_{V}} = 1.4 = \frac{7}{5}$
substituting in Eq $(i)$ ,
$\frac{7}{5} C_{V} - C_{V} = R$
$\Rightarrow \frac{2}{5} C_{V} = R$
Or, $C_{V} = \frac{5 R}{2}$ and $C_{p} = C_{V} + R = \frac{7 R}{2}$
$\Rightarrow γ = 1.4$ represents that the gas is diatomic.

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Heat Capacity

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For a gas γ=1.4. Then atomicity, Cp and CV respectively of the gas are

The correct option is C Diatomic, 7R2,5R2Given: γ=1.4 Cp−CV=R ...(i) & γ=CpCV ⇒CpCV=1.4=75 substituting in Eq (i), 75CV−CV=R ⇒25CV=R Or, CV=5R2 and Cp=CV+R=7R2 ⇒γ=1.4 represents that the gas is diatomic.

For a gas $γ = 1.4$ . Then atomicity, $C_{p}$ and $C_{V}$ respectively of the gas are