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One mole of diatomic gas is being heated in a closed tank from 300K up to 1000 K. During the process part of the molecules dissociate. At 1000 K the energy of the diatomic molecules are only half of that of the whole gas. By what factor has the gas pressure increased $(P_{f i n a l} / P_{i n i t i a l})$ ? (The oscillation of the molecules are not to be taken in account).

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$\frac{160}{33}$

$\frac{16}{11}$

$\frac{3}{2}$

$\frac{2}{3}$

answer is A.

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Detailed Solution

Let n moles of diatomic gas dissociate into monoatomic. Then mono 2n moles and dia 1 – n moles $n = \frac{5}{11}$
$\frac{P_{f i n a l}}{P_{i n i t i a l}} = \frac{160}{33}$

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