The poisson's ratio for $O_{2}$ is $1.4$ . Which of the following are correct for $O_{2}$ ?

c_{v} = 5 c a l K^{- 1} m o l^{- 1}

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C_{v} = 0.156 c a l K^{- 1} g^{- 1}

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c_{p} = \frac{R γ}{γ - 1}

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c_{v} = \frac{R}{(γ - 1)}

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Solution

The correct options are
A $c_{v} = 5 c a l K^{- 1} m o l^{- 1}$
B $c_{p} = \frac{R γ}{γ - 1}$
C $C_{v} = 0.156 c a l K^{- 1} g^{- 1}$
D $c_{v} = \frac{R}{(γ - 1)}$
$\frac{c_{p}}{c_{v}} = 1.4 = γ$
$c_{p} - c_{v} = R$
$∴$ $c_{v} = \frac{R}{γ - 1}$ and similarly $c_{p} - \frac{c_{p}}{γ} = R$
$∴$ $c_{v} = \frac{2}{0.4} = 5 c a l K^{- 1} m o l^{- 1}$ $∴$ $c_{p} = \frac{γ \cdot R}{(γ - 1)}$
Also, $C_{v} = \frac{2}{0.4 \times 32} = 0.156 c a l K^{- 1} g^{- 1}$

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