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Studiot said:How do you think the filament in a halogen source achieves its different colour temperature, if it is at the same temperature as the one in a standard bulb?
No-one has said it would be at the same temperature. Quite the opposite.
But it might be as 'hot' as a filament in a standard bulb, that is; same J, different K.
You seem to be labouring under the impression that the filaments would be the same size. Just figure that the incandescent one is twice the size of the halogen one... same heat flux, but arising from twice the differential temperature!...