Final answer:
To find the specific heat of an unknown metal, the formula q = m × c × ΔT is used, where q is the heat absorbed, m is the metal's mass, c is specific heat, and ΔT is the temperature change. By substituting the known values into the equation, the specific heat can be calculated and compared to known values to potentially identify the metal.
Step-by-step explanation:
The specific heat of a metal is determined through a process in which the metal's mass, the amount of heat absorbed, and the temperature change are known variables. To calculate the specific heat (c) of an unknown metal, we use the formula:
q = m × c × ΔT
where q is the heat absorbed, m is the mass of the metal, c is the specific heat capacity, and ΔT is the temperature change. Let's apply this to the provided scenario where a 348 g piece of metal absorbs 6.64 kJ of heat and its temperature increases from 22.4 °C to 43.6 °C. We first convert 6.64 kJ to Joules (since specific heat is typically in J/g°C), resulting in 6640 J. The temperature change (ΔT) is 43.6 °C - 22.4 °C = 21.2 °C. We can then arrange the formula to solve for the specific heat (c):
c = q / (m × ΔT) = 6640 J / (348 g × 21.2 °C)
After performing the calculation, we will obtain the specific heat of the metal. This value can then be compared to known specific heats to suggest the metal's possible identity.