A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{v}}}$ of the mixture is

JEE Main · 2005 · 08 May 2005 · Offline · Heat & Thermodynamics

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio

\frac{C _{P}}{C _{v}}

of the mixture is

(A)1.59
(B)1.62✓ Correct
(C)1.4
(D)1.54

Answer: (B)

Solution

Count the moles: helium gives

\frac{16}{4} = 4

mol with

C_{v} = \frac{3 R}{2}

, and oxygen gives

\frac{16}{32} = 0.5

mol with

C_{v} = \frac{5 R}{2}

. The mixture's molar

C_{v}

is the mole-weighted average,

C_{v} = \frac{4 \cdot \frac{3 R}{2} + 0.5 \cdot \frac{5 R}{2}}{4.5} = \frac{6 R + 1.25 R}{4.5} = \frac{29 R}{18}

. Then

C_{p} = C_{v} + R = \frac{47 R}{18}

, so

γ = \frac{C _{p}}{C _{v}} = \frac{47}{29} \approx 1.62

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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