Respuesta :
Answer: The final temperature of nickel and water is [tex]25.2^{o}C[/tex].
Explanation:
The given data is as follows.
Mass of water, m = 55.0 g,
Initial temp, [tex](t_{i}) = 23^{o}C[/tex],
Final temp, [tex](t_{f})[/tex] = ?,
Specific heat of water = 4.184 [tex]J/g^{o}C[/tex],
Now, we will calculate the heat energy as follows.
q = [tex]mS \Delta t[/tex]
= [tex]55.0 g \times 4.184 J/g^{o}C \times (t_{f} - 23^{o}C)[/tex]
Also,
mass of Ni, m = 15.0 g,
Initial temperature, [tex]t_{i} = 100^{o}C[/tex],
Final temperature, [tex]t_{f}[/tex] = ?
Specific heat of nickel = 0.444 [tex]J/g^{o}C[/tex]
Hence, we will calculate the heat energy as follows.
q = [tex]mS \Delta t[/tex]
= [tex]15.0 g \times 0.444 J/g^{o}C \times (t_{f} - 100^{o}C)[/tex]
Therefore, heat energy lost by the alloy is equal to the heat energy gained by the water.
[tex]q_{water}(gain) = -q_{alloy}(lost)[/tex]
[tex]55.0 g \times 4.184 J/g^{o}C \times (t_{f} - 23^{o}C)[/tex] = -([tex]15.0 g \times 0.444 J/g^{o}C \times (t_{f} - 100^{o}C)[/tex])
[tex]t_{f} = \frac{25.9^{o}C}{1.029}[/tex]
= [tex]25.2^{o}C[/tex]
Thus, we can conclude that the final temperature of nickel and water is [tex]25.2^{o}C[/tex].
The final temperature of water and nickel has been 25.2 degrees Celsius.
The specific heat has been defined as the amount of heat required to raise the temperature of 1 gram of substance by 1 degree Celsius.
The specific heat (c) has been expressed as:
[tex]q=mc\Delta T[/tex]
Where, the heat required by the object has been q.
The mass of the sample has been m
The change in temperature has been, [tex]\Delta T=\rm Final\;Temperature-Initial\;Temperature[/tex]
Computation for the final temperature of Nickel
The heat lost by nickel has been given as:
[tex]q_{lost}=150\;\times\;0.444\;\times\;(\rm Final\;temperature\;-\;100)\\[/tex]
The heat gained by the water sample has been given as:
[tex]q_{gain}=55\;\times\;4.184\;\times\;(\rm Final \;temperature-23)[/tex]
Since, heat gain has been equivalent to heat lost. Substituting the values as:
[tex]q_{gain}=q_{lost}\\55\;\times\;4.184\;\times\;(\rm Final\;temperature-23)=15\;\times\;0.444\;\times\;(Final\;temperature-100)[/tex]
Simplifying the equation as:
[tex]230.12\;(\rm Final\;temperature-23)=66.6\;(Final\;tempertaure-100)\\Final temperature=25.2\;^\circ C[/tex]
The final temperature of water and nickel has been 25.2 degrees Celsius.
Learn more about specific heat, here:
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