You pour 250 g of tea into a Styrofoam cup, initially at 80? C and stir in a little sugar using a 100-g aluminum 20? C spoon and leave the spoon in the cup. Assume the specific heat of tea is 4180 J/kg? C and the specific heat of aluminum is 900 J/kg? C.

What is the highest possible temperature of the spoon when you finally take it out of the cup?

Answer: 75ºC

Explanation:

Assuming that the Styrofoam is perfectly adiabatic, and neglecting the effect of the sugar on the system, the heat lost by the tea, can only be transferred to the spoon, reaching all the system to a final equilibrium temperature.

If the heat transfer process is due only to conduction, we can use this empirical relationship for both objects:

Qt = ct. mt. (tfn - ti)

Qs = cs. ms. (ti - tfn)

If the cup is perfectly adiabatic, it must be Qt = Qs

Using the information provided, and solving for tfinal, we get:

tfinal = (83,600 + 1,800) / (90 + 1045) ºC

tfinal = 75º C