A metal is thought to be titanium or aluminum. When 4.7 g of the metal absorbs 11 J, its temperature rises by 4.5 °C. (3.6) b. Would you identify the metal as titanium or aluminum (see TABLE 3.11)?

Verified step by step guidance

1. Identify the formula for specific heat capacity: q = mcΔT, where q is the heat absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
2. Rearrange the formula to solve for the specific heat capacity (c): c = q / (mΔT).
3. Substitute the given values into the formula: q = 11 J, m = 4.7 g, and ΔT = 4.5 °C.
4. Calculate the specific heat capacity using the substituted values.
5. Compare the calculated specific heat capacity with the specific heat capacities of titanium and aluminum from Table 3.11 to identify the metal.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius. It is a crucial property for identifying materials, as different metals have distinct specific heat capacities. In this case, knowing the specific heat capacities of titanium and aluminum will help determine which metal is present based on the heat absorbed and the temperature change.

Heat Transfer Equation

The heat transfer equation, often expressed as Q = mcΔT, relates the heat absorbed or released (Q) to the mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation allows us to calculate the specific heat capacity of the unknown metal by rearranging the formula to c = Q/(mΔT), which is essential for identifying whether the metal is titanium or aluminum based on the given data.

Comparison of Specific Heat Capacities

To identify the metal, we compare the calculated specific heat capacity of the sample with the known specific heat capacities of titanium and aluminum. By using the values from the provided table, we can determine which metal's specific heat capacity closely matches our calculated value. This comparison is a fundamental step in the identification process, as it directly links the experimental data to known material properties.