## Interview Question

Product Design Engineer Interview

-Cupertino, CA

# We have a cup of hot coffee and a small cold milk out of the fridge. The room temperature is in between these two. When should we add milk to coffee to get the coolest combination earliest ( at the beginning, in the middle, or at the end)?

23

At the beginning. They are not asking inserting at beginning or end.(Question is when and not where) If you add at start, it will have max. temperature difference and it will cool max. At end, all will be anyway at room temperature so will not have any difference.

SK on

1

Apple likes the answer: At the end. I was at the onsite interview. The engineering director asked me this question. He likes the answer "at the end". But, he said he wasn’t sure. He said he doesn’t know the answer to that question either. So, in other words they are asking you questions that they don’t know the answer either.

Anonymous on

1

If you do the math, it should be in the middle. The system is a first order system so that it reaches to steady states takes 4*time constant. The time constant is Ah/mCp. Based on this, those two will reach steady states based on their own surface Area (For convection) and mass at different rates. Once one of them reach to the steady state, you should mix them.

Anonymous on

1

Wouldn’t it be when the coffee reaches room temperature?

Anonymous on

9

At the end. Base on formulas of convection, the higher the surface area ( coffee ) and the higher the temperature difference, the rate of heat transfer increases. and base on formulas of conduction, as soon as we add the milk the mixture temperature drops. So now if we wait to last minute, the rate of change in temperature of coffee will be faster than milk therefore the mixture at the last second will give us a lower temperature faster.

Anonymous on