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A certain mass of an ideal diatomic gas contained in a closed vessel is heated; it is observed that the temperature remains constant: however, half the amount of gas gets dissociated; the ratio of the heat supplied to the gas initial internal energy of the gas will be

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1 : 4

1 : 5

1 : 10

1 : 2

answer is D.

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Detailed Solution

$U_{1} = n (\frac{5 R}{2}) T$

and $U_{2} = \frac{n}{2} (\frac{5 R}{2}) T + \frac{2 n}{2} (\frac{3 n}{2}) T = n (\frac{11 R}{4}) T$

$U_{2} = U_{1} + Q$

$∴ \frac{Q}{U_{1}} = \frac{U_{2}}{U_{1}} - 1 = \frac{11}{10} - 1 = \frac{1}{10}$

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