To calculate the amount of heat absorbed by the spoon, we can use the formula Q = mc∆T, where Q represents heat, m represents mass, c represents specific heat capacity, and ∆T represents the change in temperature.
First, let's find the change in temperature (∆T) of the spoon:
∆T = final temperature - initial temperature
∆T = 89.0°C - 20.0°C
∆T = 69.0°C
The mass of the spoon is given as 50.0g, and since silver is a relatively good conductor of heat, we can assume that the specific heat capacity (c) of the spoon is equal to the specific heat capacity of silver, which is 0.235 J/g°C.
Now we can calculate the amount of heat absorbed by the spoon by plugging the values into the formula:
Q = mc∆T
Q = (50.0g)(0.235 J/g°C)(69.0°C)
Q = 808.5 J
Therefore, the spoon absorbs approximately 808.5 J of heat from the coffee to reach a temperature of 89.0°C.