Final answer:
To determine the specific heat of the unknown metal, the heat absorbed is converted to joules, the change in temperature is calculated, and these values are applied to the specific heat formula. The obtained specific heat can be compared with known metals to predict the identity of the metal.
Step-by-step explanation:
The question involves calculating the specific heat of a metal using the amount of heat absorbed and the change in temperature. According to the provided data, an unknown metal weighs 217 grams and absorbs 1.43 kilojoules (kJ) of heat, causing its temperature to rise from 24.5 °C to 39.1 °C. To find the specific heat (c), the formula c = q / (m × ΔT) can be used, where q is the heat absorbed, m is the mass, and ΔT is the change in temperature.
To perform the calculation:
- Convert the heat absorbed from kJ to joules (J) since the specific heat is typically given in J/(g°C). There are 1000 J in 1 kJ, so the heat absorbed is 1.43 kJ × 1000 = 1430 J.
- Calculate the change in temperature (ΔT) by subtracting the initial temperature from the final temperature, which is 39.1 °C - 24.5 °C = 14.6 °C.
- Apply the values to the specific heat formula: c = 1430 J / (217 g × 14.6 °C) = 1430 J / 3168.2 g°C = 0.4515 J/(g°C).
Once the specific heat is known, it can be compared with known values for specific heats of metals to predict the identity of the metal. The given value (0.4515 J/(g°C)) closely matches the specific heat of known metals, which can help in identifying the metal in question.