thermodynamics - What is more efficient: Add milk, and then heat up coffee in the microwave, or microwave than milk?

Adding milk first increases the volume to heat and lowers average temerature, but adding it afterwards seems to have similar effects. How can you compare the two?

Answer

By adding milk first you reduce heat loss during heating due to lower average temperature. The rate of heat transfer to the surroundings depends on the difference in temperature between the object and its surroundings, so lower average temperature-> less energy lost to the surroundings.

So if you add milk first, you will get higher temperature at the end.

But personally, I prefer to add milk after, as it's more sensetive to overheating. You can heat cofee to 100C without any damage to it.