Answer :
Answer: The final temperature of the solution is [tex]80.14^oC[/tex]
Explanation:
The amount of heat released by coffee will be absorbed by aluminium spoon.
Thus, [tex]\text{heat}_{absorbed}=\text{heat}_{released}[/tex]
To calculate the amount of heat released or absorbed, we use the equation:
[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]
Also,
[tex]m_1\times c_1\times (T_{final}-T_1)=-[m_2\times c_2\times (T_{final}-T_2)][/tex] ..........(1)
where,
q = heat absorbed or released
[tex]m_1[/tex] = mass of aluminium = 39 g
[tex]m_2[/tex] = mass of coffee = 166 g
[tex]T_{final}[/tex] = final temperature = ?
[tex]T_1[/tex] = temperature of aluminium = [tex]24^oC[/tex]
[tex]T_2[/tex] = temperature of coffee = [tex]83^oC[/tex]
[tex]c_1[/tex] = specific heat of aluminium = [tex]0.904J/g^oC[/tex]
[tex]c_2[/tex] = specific heat of coffee= [tex]4.1801J/g^oC[/tex]
Putting all the values in equation 1, we get:
[tex]39\times 0.904\times (T_{final}-24)=-[166\times 4.1801\times (T_{final}-83)][/tex]
[tex]T_{final}=80.14^oC[/tex]
Hence, the final temperature of the solution is [tex]80.14^oC[/tex]