A copper calorimetric cup with a mass of 100g contains 96g of water at 13 C. If 70g of a substance at 84 C is dropped into the cup, the temperature increases to 20 C. Find the specific heat capacity of the substance.
To find the specific heat capacity of the substance, we can use the principle of conservation of energy. The energy gained by the substance is equal to the energy lost by the water and the calorimetric cup.
First, let's calculate the heat gained by the water and the cup. We will use the formula:
Q = mcΔT
Where:
Q is the heat gained/lost
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
For the water and the cup, the heat gained (Qwater-cup) can be calculated as follows:
Qwater-cup = (mwater + mcup) * cwater-cup * ΔTw-cup
Given:
mwater = 96g (mass of water)
mcup = 100g (mass of copper calorimetric cup)
ΔTw-cup = Tfinal - Tinitial = (20C - 13C) = 7C (change in temperature)
We need to find cwater-cup (specific heat capacity of the water-cup mixture) in order to calculate the heat gained by the water and the cup.
We know that the specific heat capacity of water is 4.18 J/g°C.
Thus,
Qwater-cup = (96g + 100g) * cwater-cup * 7C
Now let's calculate the heat gained by the substance (Qsubstance). Using the same formula as before:
Qsubstance = msubstance * csubstance * ΔTsubstance
Given:
msubstance = 70g (mass of the substance)
ΔTsubstance = Tfinal - Tinitial = (20C - 84C) = -64C (change in temperature)
We need to find csubstance (specific heat capacity of the substance) in order to calculate the heat gained by the substance.
Now, we can set up the conservation of energy equation:
Qwater-cup + Qsubstance = 0
Substituting the values and rearranging the equation:
(96g + 100g) * cwater-cup * 7C + 70g * csubstance * -64C = 0
Simplifying further:
196g * cwater-cup * 7C - 70g * csubstance * 64C = 0
Solving for csubstance:
70g * csubstance * 64C = 196g * cwater-cup * 7C
csubstance = (196g * cwater-cup * 7C) / (70g * 64C)
Plugging in the value of the specific heat capacity of water, cwater = 4.18 J/g°C:
csubstance = (196g * 4.18 J/g°C * 7C) / (70g * 64C)
csubstance = 0.81 J/g°C
Therefore, the specific heat capacity of the substance is 0.81 J/g°C.