Q140 / 160 · TS EAMCET 2021 (06 Aug Shift 2) · Physics

A cylinder consists of a gas mixture of helium and oxygen. If the mass of helium is $4 \mathrm{~g}$ and the mass of oxygen is $32 \mathrm{~g}$, then the ratio of specific heat of the mixture $\left(C_p / C_V\right)$

  • A
    2/3
  • Correct answer
    B
    3/2
  • C
    1/2
  • D
    1/3

Solution

Mass of helium, $m_{\mathrm{He}}=4 \mathrm{~g}$ Mass of oxygen, $m_{\mathrm{O}}=32 \mathrm{~g}$ Helium is a monoatomic gas. $\therefore$ Degrees of freedom, $f_1=3$ Oxygen is a diatomic gas. $\therefore$ Degrees of freedom, $f_2=5$ $4 \mathrm{~g}$ helium contains $N_1=N_A=6.023 \times 10^{23}$ number of molecules $32 \mathrm{~g}$ oxygen contains $N_2=N_A$ number of molecules. (As atomic mass of oxygen is $16 \mathrm{~g}$ ) $$ \begin{aligned} \therefore \quad \frac{C_p}{C_V} & =\gamma \\ & =\frac{N_1\left(2+f_1\right)+N_2\left(2+f_2\right)}{N_1 f_1+N_2 f_2} \\ & =\frac{N_A(2+3)+N_A(2+5)}{3 N_A+5 N_A} \\ & =\frac{5+7}{3+5}=\frac{12}{8}=\frac{3}{2} \end{aligned} $$

Hence, the correct answer is option: 'B'.

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