A 50.0g sliver spoon at 20.0 degrees celsius is placed in a cup of cofee at 90.0 degrees celsius. How much heat does the spoon absorb from the cofee to reach a temperature of 89.0 degrees celsius?
Please explain...
They don't tell you the mass of the coffee, but you know the mass of the spoon. The heat lost by the coffee equals the heat absorbed by the spoon. Call it Q
Q = (spoon mass) x (silver specfic heat) x (temperature rise of spoon)
The specific heat of silver is 0.234 Joules/(grams degC)
To find the amount of heat absorbed by the spoon, we can use the formula:
Q = mcΔT
Where:
Q is the heat absorbed by the spoon.
m is the mass of the spoon.
c is the specific heat capacity of silver.
ΔT is the change in temperature.
Given:
Mass of the spoon (m) = 50.0 g
Initial temperature of the spoon (T1) = 20.0 °C
Final temperature of the spoon (T2) = 89.0 °C
Specific heat capacity of silver (c) = 0.24 J/g°C
First, we need to calculate the change in temperature (ΔT) of the spoon:
ΔT = T2 - T1
ΔT = 89.0 °C - 20.0 °C
ΔT = 69.0 °C
Now, we can substitute the known values into the formula:
Q = mcΔT
Q = (50.0 g)(0.24 J/g°C)(69.0 °C)
Calculating this:
Q = 828 J
Therefore, the spoon absorbs 828 Joules of heat from the coffee to reach a temperature of 89.0 degrees Celsius.
To find out how much heat the silver spoon absorbs from the coffee, we can use the equation:
Q = m * c * ΔT
Where:
Q = amount of heat absorbed (in Joules)
m = mass of the silver spoon (in grams)
c = specific heat capacity of silver (0.235 J/g°C)
ΔT = change in temperature (final temperature - initial temperature) (in °C)
First, let's calculate the change in temperature of the silver spoon:
ΔT = final temperature - initial temperature
ΔT = 89.0°C - 20.0°C
ΔT = 69.0°C
Now, we can substitute the values into the equation:
Q = 50.0g * 0.235 J/g°C * 69.0°C
Calculating the value:
Q = 808.5 J
Therefore, the silver spoon absorbs 808.5 Joules of heat from the coffee to reach a temperature of 89.0 degrees Celsius.