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## Cozy Ice Cream

Heat is constantly flowing all around us: a roaring fire transfers heat to its surroundings, a mother cow transfers heat to her cuddling calves, and heat transfers between your skin and the air that it touches.

One way that heat flows is by conduction: heat flowing through matter by way of direct contact. When you hold a mug of hot tea or a glass of ice water, heat conducts through the wall of the cup between your hand and the liquid.

The net conductive heat flow $Q$ through an object is proportional to the difference in temperatures across the object and the inherent thermal conductivity $k$ of the object, a measure of how readily the material conducts heat:

$Q \propto k\times \Delta T.$

One place you see this relationship in action is when you wrap yourself in a blanket on a chilly day. Unless you're exercising, your body releases a more or less constant flow of heat to its surroundings.

But when you wrap yourself in a blanket, you're introducing a barrier to heat flow, corresponding to a lower $k.$ In turn, less heat escapes, raising your skin temperature until the larger $\Delta T$ across the blanket balances out the lower $k.$

Since your skin temperature has risen, thermoreceptors in your skin sense the increase in temperature and you feel nice and toasty.

# Today's Challenge

You take two cartons of ice cream out of the freezer, leaving them both on the counter, but wrapping one in a nice cozy blanket.

Which carton of ice cream will melt first?

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