JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Heat & Thermodynamics

Two moles of an ideal gas with

\frac{C _{P}}{C _{V}} = \frac{5}{3}

are mixed with 3 moles of another ideal gas with

\frac{C _{P}}{C _{V}} = \frac{4}{3}

. The value of

\frac{C _{P}}{C _{V}}

for the mixture is:

(A)1.42✓ Correct
(B)1.47
(C)1.45
(D)1.50

Answer: (A)

Solution

For a mixture of ideal gases the molar heat capacities add, which we can write as

\frac{n _{1} + n _{2}}{γ _{mix} - 1} = \frac{n _{1}}{γ _{1} - 1} + \frac{n _{2}}{γ _{2} - 1}

. Putting

n_{1} = 2, γ_{1} = \frac{5}{3}

and

n_{2} = 3, γ_{2} = \frac{4}{3}

gives

\frac{5}{γ _{mix} - 1} = \frac{2}{2/3} + \frac{3}{1/3} = 3 + 9 = 12

, so

γ_{mix} - 1 = \frac{5}{12}

and

γ_{mix} = \frac{17}{12} \approx 1.42

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option

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