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As far as heat conduction is concerned, the vibrational energy of the particles would be transformed from one particle to the other. So as heat is gained then the amplitude of vibration increases.

In case of electrical conductivity, charged particles move in the direction of the electric field.

In solids the negatively charged electrons get drifted opposite to the direction of the field.

In liquids, both positive ions and negative ions are the cause for the conduction of electricity through liquids.

In case of gases too, the same positive and negative ions are the cause.

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