For a filament lamp that is operating normally such that the temperature is constant, the rate of change in internal energy of the system is zero.
This would mean that rate of net heat transfer to the system + rate of work done on the system = 0
I can understand why rate of work done on the system will be positive since the electrons will do positive work on the ions in the filament as it collides with them. However, why is it that rate of heating of the filament is negative?
Wouldn't the rate of heating be zero? Since rate of thermal energy supplied by the source = rate of heat loss to surrounding by radiation
Best Answer
You have correctly deduced that the rate of heat transfer to the system is negative. This means that heat is leaving the system (that is leaving the filament).
What is heat? Heat is energy in transit from a higher temperature region to a lower temperature region due to the temperature difference.
In this case the filament is very hot and the surroundings are much cooler. There is a net flow of energy, largely in the form of infrared and visible electromagnetic radiation, from the filament to the surroundings. This is the heat flow from the system, that is heat leaving the system.
[Addendum Your confusion may be due to (understandable) confusion over words. I've given (above) the scientific meaning of 'heat'. You are using 'heating' to mean 'making hotter'. This is the everyday use of the word. And indeed, it's not silly, because usually supplying heat to something does make it hotter! But not always. You can supply heat to a pot of boiling water, but the water stays at 100 °C. And the electrically powered filament loses heat to its surroundings without getting cooler. In thermodynamics, avoid using 'heating' if you mean making hotter. You may use it to mean supplying heat, but it's safer to say 'supplying heat'!]