A 5.0g silver spoon at 20.0C is placed in a cup of coffee at 90.0C. How much heat does the spoon absorb from the coffee to reach a temperature of 89.0C?
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5 g is much too low a mass for a coffee spoon
To calculate the heat absorbed by the silver spoon, we can use the formula:
Q = mcΔT
Where:
Q = Heat absorbed
m = Mass of the spoon
c = Specific heat capacity of silver
ΔT = Change in temperature
First, let's calculate the change in temperature using the formula:
ΔT = Tf - Ti
Where:
Tf = Final temperature (89.0 ºC)
Ti = Initial temperature (20.0 ºC)
ΔT = 89.0 ºC - 20.0 ºC
= 69.0 ºC
Next, we need the specific heat capacity of silver. The specific heat capacity of silver is approximately 0.235 J/g°C.
Now, with all the values, we can calculate the heat absorbed:
Q = mcΔT
= (5.0g)(0.235 J/g°C)(69.0 ºC)
Calculating further:
Q = 816.75 J
Therefore, the spoon absorbs approximately 816.75 Joules of heat from the coffee to reach a temperature of 89.0 ºC.
To find the amount of heat absorbed by the spoon, we can use the heat transfer equation:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
First, let's find the change in temperature for the spoon:
ΔT = 89.0°C - 20.0°C = 69.0°C
The specific heat capacity of silver is 0.235 J/g°C. Now we can calculate the heat absorbed by the spoon:
Q = (mass of spoon) x (specific heat capacity of silver) x (change in temperature)
mass of spoon = 5.0 g
specific heat capacity of silver = 0.235 J/g°C
change in temperature = 69.0°C
Q = (5.0 g) x (0.235 J/g°C) x (69.0°C)
Now let's calculate the value of Q:
Q = 809.775 J
Therefore, the spoon absorbs approximately 809.775 J of heat from the coffee to reach a temperature of 89.0°C.