Answer:
The temperature of the metal is  [tex]T_m = 376.8 ^o C[/tex]
Explanation:
From the question we are told that
   The mass of the metal is  [tex]M = 60 \ kg[/tex]
   The specific heat of the metal is  [tex]c_p = 0.1027 kcal/(kg \cdot ^oC)[/tex]
    The mass of the oil is [tex]M_o = 810 \ kg[/tex]
    The temperature of the oil is  [tex]T_o = 35^oC[/tex]
    The specific heat of oil is  [tex]c_o = 0.7167 kcal/(kg \cdot ^oC )[/tex]
    The equilibrium temperature is [tex]T_e = 39 ^oC[/tex]
According to the law of energy conservation
   Heat lost by metal  =  heat gained by the oil
So Â
  The quantity  of heat lost by the metal is mathematically represented as
        [tex]Q = - Mc_p \Delta T[/tex]
=> Â Â Â Â Â Â [tex]Q = -Mc_p (T_m - T_c)[/tex]
Where [tex]T_ m[/tex] Â the temperature of metal before immersion
The negative sign show heat lost
The quantity  of gained t by the metal is mathematically represented as   Â
      [tex]Q = M_o c_o \Delta T[/tex]
=> Â Â Â Â [tex]Q = M_o c_o (T_c - T_o)[/tex]
So Â
     [tex]Mc_p (T_m - T_c) = M_o c_o (T_c - T_o)[/tex]
substituting values
     [tex]- 60 * 0.1027 (T_m - 39) = 810 * 0.7167 * (39 - 35)[/tex]
=> Â Â Â [tex]T_m = 376.8 ^o C[/tex]
    Â
