Answer:
We can use the formula for heat absorbed or released by a substance to calculate the specific heat of the metal:
Q = mcΔT
where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.
We know that the water sample absorbed 2,851 J of energy from the metal. We also know that the mass of the metal is 42.6 g, and the change in temperature is:
ΔT = (40.0°C - 209°C) = -169°C
(Note that we use the Celsius scale here, so the change in temperature is negative.)
Substituting these values into the formula, we get:
2851 J = (42.6 g) * c * (-169°C)
Solving for c, we get:
c = 2851 J / [(42.6 g) * (-169°C)]
c = 0.388 J/(g°C)
Therefore, the specific heat of the metal is 0.388 J/(g°C).