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7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K

Question

7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at $\frac{T}{3} K$ and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was $\frac{5 T}{6} K,$ then gas B is ? (Assuming all modes of energy are active)

monoatomic

diatomic

triatomic

tetra atomic

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7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at

\frac{T}{3} K

and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was

\frac{5 T}{6} K,

then gas B is ? (Assuming all modes of energy are active)

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Text solutionVerified

Answer: bSolution: (b)

C_{v}

of gas

A = \frac{3}{2} R + \frac{3}{2} R + 6 R = 9 R

Let

C_{v}

of gas

B = X

Heat lost by gas

A = 7 \times 9 R \times (T - \frac{5 T}{6})

Heat gained by gas

B = 6 X (\frac{5 T}{6} - \frac{T}{3})

\Rightarrow 63 R (\frac{T}{6}) = 6 X (\frac{T}{2}) = X = \frac{7}{2} R,

∴

gas is diatomic

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Question Text	7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at $\frac{T}{3} K$ and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was $\frac{5 T}{6} K,$ then gas B is ? (Assuming all modes of energy are active)
Answer Type	Text solution:1
Upvotes	151