To solve this problem it is necessary to apply the concepts related to the conservation of energy and heat transferred in a body.
By definition we know that the heat lost must be equal to the heat gained, ie
Where,
Q = Heat exchange
The heat exchange is defined as
Where,
Specific heat
m = mass
Change in Temperature
Therefore replacing we have that
Replacing with our values we have that
Therefore the highest possible temperature of the spoon when you finally take it out of the cup is 75.24°C