Answer :
Taking into account the definition of calorimetry, the specific heat of aluminum is 0.898 J/gC.
Definition of calorimetry
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
When heat added or removed from a substance causes a temperature change in it without affecting its molecular structure, it is called sensible heat.
The expression that allows to calculate heat exchanges is:
Q = c× m× ΔT
where:
- Q is the heat exchanged by a body of mass m.
- c is the specific heat substance.
- ΔT is the temperature variation.
Specific heat of aluminum
In this case, you know:
- For aluminum:
- Mass of aluminum = 28.4 g
- Initial temperature of aluminum= 39.4 °C
- Final temperature of aluminum= 23 ºC
- Specific heat of aluminum = Unknown
- For water:
- Mass of water = 50 g
- Initial temperature of water= 21 ºC
- Final temperature of water= 23 ºC
- Specific heat of water = 4.186 J/gC
Replacing in the expression to calculate heat exchanges:
- For aluminum: Qaluminum= Specific heat of aluminum × 28.4 g× (23 C - 39.4 C)
- For water: Qwater= 4.186 J/gC× 50 g× (23 C - 21 C)
If two isolated bodies or systems exchange energy in the form of heat, the quantity received by one of them is equal to the quantity transferred by the other body. That is, the total energy exchanged remains constant, it is conserved.
Then, the heat that the gold gives up will be equal to the heat that the water receives. Therefore:
- Qaluminum = + Qwater
- Specific heat of aluminum × 28.4 g× (23 C - 39.4 C)= 4.186 J/gC× 50 g× (23 C - 21 C)
Solving:
Specific heat of aluminum × 465.76 gC= 418.6 J
Specific heat of aluminum=418.6 J÷ 465.76 gC
Specific heat of aluminum= 0.898 J/gC
Finally, the specific heat of aluminum will be 0.898 J/gC.
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