Answer : The specific heat of the metal is, [tex]2178.67J/kg^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 metal = ?
[tex]c_2[/tex] = specific heat of ice = [tex]2000J/kg^oC[/tex]
[tex]m_1[/tex] = mass of metal = 1.00 kg
[tex]m_2[/tex] = mass of ice = 1.00 kg
[tex]T_f[/tex] = final temperature of mixture = [tex]-8.88^oC[/tex]
[tex]T_1[/tex] = initial temperature of metal = [tex]5.00^oC[/tex]
[tex]T_2[/tex] = initial temperature of ice = [tex]-24.0^oC[/tex]
Now put all the given values in the above formula, we get:
[tex](1.00kg)\times c_1\times (-8.88-5.00)^oC=-[(1.00kg)\times 2000J/kg^oC\times (-8.88-(-24.0))^oC][/tex]
[tex]c_1=2178.67J/kg^oC[/tex]
Therefore, the specific heat of the metal is, [tex]2178.67J/kg^oC[/tex]
