Final answer:
The specific heat of the metal is calculated using the formula q = mcΔT. With the energy absorbed, mass, and temperature change known, the specific heat is found to be approximately 0.1375 J/g°C.
Step-by-step explanation:
The student asked about calculating the specific heat of a metal given the energy absorbed by a water sample from the metal and the change in temperature of the metal. To find the specific heat capacity (c) of the metal, we can use the formula q = mcΔT, where q is the heat absorbed or released, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The energy absorbed by the water is given as 3,135 Joules, which is also the energy released by the metal since energy is conserved. The mass of the metal is given as 63.0 grams, and the change in temperature (ΔT) is (382°C - 20.0°C), thus ΔT is 362°C. Plugging these values into the formula q = mcΔT, we can rearrange to solve for c,
c = q / (mΔT)
Substitute the values:
c = 3,135 J / (63.0 g × 362°C) = 3,135 J / (22,806 g°C) = 0.1375 J/g°C
Therefore, the specific heat of the metal is approximately 0.1375 J/g°C.