Respuesta :
Answer : The metal used was iron (the specific heat capacity is [tex]0.449J/g^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 unknown metal = ?
[tex]c_2[/tex] = specific heat of water = [tex]4.184J/g^oC[/tex]
[tex]m_1[/tex] = mass of unknown metal = 150 g
[tex]m_2[/tex] = mass of water = 200 g
[tex]T_f[/tex] = final temperature of water = [tex]34.3^oC[/tex]
[tex]T_1[/tex] = initial temperature of unknown metal = [tex]150.0^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]150g\times c_1\times (34.3-150.0)^oC=-200g\times 4.184J/g^oC\times (34.3-25.0)^oC[/tex]
[tex]c_1=0.449J/g^oC[/tex]
Form the value of specific heat of unknown metal, we conclude that the metal used in this was iron (Fe).
Therefore, the metal used was iron (the specific heat capacity is [tex]0.449J/g^oC[/tex]).
