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Question

A container is filled with 20 mole of an ideal diatomic gas at absolute temperature T. When heat is supplied to it, the temperature remain constant but 8 mole of the gas disassociates into atoms. The heat energy supplied to the gas is

A
7RT
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B
6RT
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C
4RT
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D
5RT
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Solution

The correct option is C 4RT
Initial internal energy,
Ui=nfRT2=20×5×RT2=50RT
[for diatomic gas, f=5]
Final internal energy,
Uf=n1f1RT2+n2f2RT2
Uf=12×5×RT2+2×8×3×RT2=54RT
[if one mole of diatomic gas disassociates then two mole of monatomic gas is produced, 8X28X+8X, for diatomic gas, f=3]
Now, change in internal energy will be energy supplied to the gas,
ΔU=UfUi=54RT50RT=4RT

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