Answer:
[tex]T_{eq}=27.97\°C[/tex]
Explanation:
Hello.
In this case, for equilibrium temperature problems, it is said that the heat balance allows us to notice how the hot substance heats up the cold substance until they reach the equilibrium temperature which is a temperature that remains constant upon time. Thus, since here the hot substance is the nickel and water gains that released heat by the nickel we can write:
[tex]Q_{Zn}=-Q_{water}[/tex]
Which can be written in terms of temperatures, masses and specific heats:
[tex]m_{Zn}C_{Zn}(T_{eq}-T_{Zn})=-m_{water}C_{water}(T_{eq}-T_{water})[/tex]
Thus, solving for the equilibrium temperature we write:
[tex]T_{eq}=\frac{m_{Zn}C_{Zn}T_{Zn}+m_{water}C_{water}T_{water}}{m_{Zn}C_{Zn}+m_{water}C_{water}}[/tex]
Now, plugging in the known data, considering the mass of water 64.00-4.00=60.00 g and its initial temperature, 25.00°C, we obtain:
[tex]T_{eq}=\frac{34.10g*0.444\frac{J}{g\°C}* 77.17\°C+60.0g*4.184\frac{J}{g\°C}*25.00\°C}{34.10g*0.444\frac{J}{g\°C}+60.0g*4.184\frac{J}{g\°C}}\\\\T_{eq}=27.97\°C[/tex]
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The final temperature of water is required.
The final temperature of water is [tex]27.97^{\circ}\text{C}[/tex].
T = Equilibrium temperature
[tex]T_n[/tex] = Temperature of nickel = [tex](77.17^{\circ}\text{C}+273.15)\ \text{K}[/tex]
[tex]T_w[/tex] = Temperature of water = [tex](25^{\circ}\text{C}+273.15)\ \text{K}[/tex]
[tex]c_n[/tex] = Specific heat of nickel = [tex]0.444\ \text{J/g}^{\circ}\text{C}[/tex]
[tex]c_w[/tex] = Specific heat of water = [tex]4.184\ \text{J/g}^{\circ}\text{C}[/tex]
[tex]m_n[/tex] = Mass of nickel = 34.1 g
[tex]m_w[/tex] = Mass of water = 60 g
The heat balance of the system is given by
[tex]m_wc_w(T-T_w)=m_nc_n(T_n-T)\\\Rightarrow m_wc_wT-m_wc_wT_w=m_nc_nT_n-m_nc_nT\\\Rightarrow T=\dfrac{m_nc_nT_n+m_wc_wT_w}{m_wc_w+m_nc_n}\\\Rightarrow T=\dfrac{34.1\times 0.444\times 350.32+60\times 4.184\times 298.15}{60\times 4.184+34.1\times 0.444}\\\Rightarrow T=301.12\ \text{K}=301.12-273.15\\\Rightarrow T=27.97^{\circ}\text{C}[/tex]
The final temperature of water is [tex]27.97^{\circ}\text{C}[/tex].
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