A cup of hot coffee can be cooled by placing a cold spoon in it. A spoon of which of the following materials would be most effective for this purpose: aluminum, copper, iron, or glass? Assume all spoons have the same mass.

copper

Explanation: when a spoon is placed in a hot coffee, the coffee will cool off based on the concept of heat transfer.

The coffee is at a higher temperature compared to the spoon, hence there is conduction of heat by the spoon from the coffee.

Heat is now transfered from the coffee to the spoon, the rate of heat transfer ( for this case coffee to spoon) is dependent on some properties but for this case, the thermal conductivity is of the most important.

A material of high thermal conductivity have a very fast rate of heat transfer and a material of low thermal conductivity have a slow rate of heat transfer.

Below is the value of thermal conductivity for copper, aluminum, iron and glass.

Copper (385 w/m.K)

Aluminum (205 W/m.K)

Iron (79.5 W/m.K)

Glass (0.8 W/m.K)

It can been seen that copper has the highest value for thermal conductivity which implies that it will conduct heat faster compared to others thus cooling the coffee faster.

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: