Question

When 27.0 g of an unknown metal initially at 18.4 °C is placed in 70.0 g H₂O initially at 79.5 °C, both substances reached thermal equilibrium at 76.8 °C. Determine the specific heat capacity of the metal. The specific heat capacity of water is 4.184 J/g°C.

Answer 1

To determine the specific heat capacity of the metal, use the equation q = m · c · ΔT. The heat transferred to the metal equals the heat transferred from the water, so you can calculate the specific heat capacity of the metal using the given values.

Step-by-step explanation:

To determine the specific heat capacity of the metal, we can use the equation q = m · c · ΔT, where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. In this case, the heat transferred to the metal equals the heat transferred from the water, so we can calculate it using the equation q = mH2O · cH2O · ΔTH2O. Rearranging the equation, we find that cMetal = q / (mMetal · ΔTMetal), where q = mH2O · cH2O · ΔTH2O. Plugging in the given values, we have q = (70.0 g) · (4.184 J/g°C) · (76.8 °C - 79.5 °C) and mMetal = 27.0 g. Substituting these into the equation, we get cMetal = [(70.0 g) · (4.184 J/g°C) · (76.8 °C - 79.5 °C)] / [(27.0 g) · (76.8 °C - 18.4 °C)]. Calculating this expression gives us the specific heat capacity of the metal.