I like to eat my pie with ice cream

I love comfort food. That being said, I often find myself drooling over a piece of freshly-served toll house pie. Toll house pie is usually served hot of the oven with a huge scoop of vanilla ice cream. The heat from the pie melts the ice cream and it turns into the most wonder plate of goo.









The ice cream is very important, not only as it enhances the overall taste, but also because it balances out the heat of the pie. A piece of apple pie could potentially burn you worse because the outside cool crust often disguises the inner warm fillings. Imagine eating a  pie without the ice cream, that could burn your tongue really bad. It happened to me last night when I couldn't wait for my roommate to put a scoop of ice cream on top of our freshly-baked apple pie. Thus, it got me thinking about the relationship between energy, temperature, and heating.


The heat transfer equation Q = m cp ΔT describes the relationship between the eternal energy added Q and the change in temperature T for a mass m of food.  cp describes the specific heat capacity of the food.  cp for ice cream is 3.1 kJ/kg^oC, for apple fillings, it's 3.64 kJ/kg^oC. Assume the initial temperature of pie is 80 ^oC, and ice cream is 0 ^oC.  The mass of the pie is 30g, and the mass of ice cream is 8g. We want to find out the final temperature of the pie and ice cream.

For pie: Q= 30g*3.6kJ/kg^oC*(T-80)^oC=0.03kg*3.6kJ/kg^oC*(T-80)

For ice cream: Q=0.008kg* 3.1kj/kg^oC*(T-0)^oC

-Q pie=Qice

T=65^oC

As we can see, heat transferring between pie and ice cream makes it more pleasant to eat a pie. The similar thing can be said about adding cold milk to hot coffee to lower the overall temperature.