A container is filled with 20mole of an ideal diatomic gas at absolute temperature T. When heat is supplied to it, the temperature remain constant but 8mole 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 C4RT 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, 8X2→8X+8X, for diatomic gas, f=3] Now, change in internal energy will be energy supplied to the gas, ΔU=Uf−Ui=54RT−50RT=4RT