We know The first law of thermodynamics is the general law of conservation of energy applied to any system in which energy transfer from or to the surroundings (through heat and work) and is stated as

ΔQ = ΔU + ΔW

where ΔQ is the heat supplied to the system, ΔW is the work done by the system and ΔU is the change in internal energy of the system.

Here electric heater supplies heat to a system at a rate of 100W i.e. each second 100 J heat is supplied to the system so the heat supplied to system each second is

ΔQ = 100 J

system performs work at a rate of 75 joules per second, so work done by the system each second is

ΔW = 75 J

So putting in equation ΔQ = ΔU + ΔW

100 J = ΔU + 75 J

Or we get

ΔU = 100 J – 75 J = 25 J

So change in internal energy each second is 25 J , or we can say rate of change or increase of internal energy of system is 25 J/s