Answer:
The specific heat of B is greater than that of A.
Explanation:
The amount of heat lost by A is:
q = m C ΔT
q = (200 g) Ca (100°C - 50°C)
q = 10,000 Ca
The amount of heat gained by B is:
q = (100 g) Cb (50°C - 0°C)
q = 5,000 Cb
Since the heat lost by A = heat gained by B:
10,000 Ca = 5,000 Cb
2 Ca = Cb
So the heat capacity of B is double the heat capacity of A. Answer 5.
Taking into account the definition of calorimetry, the correct answer is option 5: The specific heat of B is greater than that of A.
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
So, the equation that allows to calculate heat exchanges is:
Q = c× m× ΔT
where Q is the heat exchanged by a body of mass m, made up of a specific heat substance c and where ΔT is the temperature variation.
In this case, you know:
Replacing in the expression to calculate heat exchanges:
For liquid A: QliquidA= [tex]c_{A}[/tex] × 200 g× (50 C - 100 C)
For liquid B: QliquidB= [tex]c_{B}[/tex] × 100 g× (50 C - 0 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 liquid A gives up will be equal to the heat that the liquid B receives. Therefore:
- QliquidA = + QliquidB
- [tex]c_{A}[/tex] × 200 g× (50 C - 100 C)= [tex]c_{B}[/tex] × 100 g× (50 C - 0 C)
Solving:
- [tex]c_{A}[/tex] × 200 g× ( - 50 C)= [tex]c_{B}[/tex] × 100 g× (50 C)
[tex]c_{A}[/tex] × 10,000 gC= [tex]c_{B}[/tex] × 5,000 gC
([tex]c_{A}[/tex] × 10,000 gC) ÷ 5,000 gC= [tex]c_{B}[/tex]
[tex]c_{A}[/tex] × 2= [tex]c_{B}[/tex]
Finally, the correct answer is option 5: The specific heat of B is greater than that of A.
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