A student places 120 g of an unknown metal at 99.9 °C into 85.88 g of water at 22.2 °C. The entire system reaches a uniform temperature of 31.5 °C. Calculate the specific heat capacity of the metal in J/g°C. The specific heat of water is 4.184 J/g°C.

Using the formula for heat transfer, the unknown specific heat capacity of a metal can be found by equating the heat lost by the metal to the heat gained by the water, and solving the resulting equation. The specific heat capacity of the given metal is approximately 0.397 J/g°C.

Explanation:

The specific heat capacity can be calculated using the formula Q= m*c*ΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The sign indicates the direction of the heat flow. In this case, the heat lost by the metal equals the heat gained by the water: -Q(metal) = Q(water).

So, (-m_metal * c_metal * ΔT_metal) = (m_water * c_water * ΔT_water). Plugging in the known values:

-(120g * c_metal * (31.5°C - 99.9°C)) = (85.88g * 4.184 J/g°C * (31.5°C - 22.2°C)).

Solving this equation, we find that the specific heat capacity of the metal, c_metal, is approximately 0.397 J/g°C.

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