Answer
$0.49\ J/g.°C$
Work Step by Step
Calculate the heat gained by water ($c_w=4.184\ J/g.°C$) using the sensible heat equation:
$q=mc\Delta T$
$q_w=100.\ g\cdot 4.184\ J/g.°C\cdot (18.3°C-15.0°C)$
$q_w=1.4\cdot10^3\ J$
Neglecting heat losses, all the heat lost by the metal is gained by the water:
$q_w+q_m=0$
$q_m=-1.4\cdot10^3\ J$
The final temperature of the metal, when it reaches thermal equilibrium with water, must be the same as the final temperature of the water, 18.3°C. Calculate the specific heat capacity of the metal using the sensible heat equation:
$q=mc\Delta T$
$-1.4\cdot10^3\ J=50.0\ g\cdot c_m\cdot (18.3°C-75.0°C)$
$c_m=\frac{-1.4\cdot10^3\ J}{-2.84\cdot10^3\ g.°C}$
$c_m=0.49\ J/g.°C$
