The amount of thermal energy gained or lost is calculated as:
thermal energy gained or lost = mass of substance x specific heat x change in temperature.
In this case, the temperature of water has increased and it has gained some thermal energy. This amount of thermal energy can be calculated as:
Thermal energy gained by water = mass of water x specific heat of water x (final temperature - initial temperature)
= 0.15 kg x 4186 J/kg/K x (21.7 - 4.1) C = 11,051.04 J
The gain in thermal energy of the water is due to thermal energy loss by the metal, which can be written as:
thermal energy lost by metal = 9 x 10^-2 x C x (96.2 - 21.7)
where C is the specific heat of the metal in J/kg/K.
Assuming no heat loss,
thermal energy lost by metal = thermal energy gained by water
or, 9 x 10^-2 x C x (96.2 - 21.7) = 11,051.04
solving the equation, we get, C = 1648.2 J/kg/K or 1.648 J/g/K
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