Respuesta :
Answer : The final temperature of the mixture is [tex]29.6^oC[/tex]
Explanation :
In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.
[tex]q_1=-q_2[/tex]
[tex]m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)[/tex]
where,
[tex]c_1[/tex] = specific heat of iron = [tex]0.499J/g^oC[/tex]
[tex]c_2[/tex] = specific heat of water = [tex]4.18J/g^oC[/tex]
[tex]m_1[/tex] = mass of iron = 39.9 g
[tex]m_2[/tex] = mass of water = [tex]Density\times Volume=1g/mL\times 50.0mL=50.0g[/tex]
[tex]T_f[/tex] = final temperature of mixture = ?
[tex]T_1[/tex] = initial temperature of iron = [tex]78.1^oC[/tex]
[tex]T_2[/tex] = initial temperature of water = [tex]25.0^oC[/tex]
Now put all the given values in the above formula, we get
[tex](39.9g)\times (0.499J/g^oC)\times (T_f-78.1)^oC=-(50.0g)\times 4.18J/g^oC\times (T_f-25.0)^oC[/tex]
[tex]T_f=29.6^oC[/tex]
Therefore, the final temperature of the mixture is [tex]29.6^oC[/tex]
