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 (seeTABLE3.11)?

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 that varies among different materials, allowing us to identify substances based on how they respond to heat. In this question, the specific heat capacities of titanium and aluminum will be compared to determine which metal corresponds to the observed temperature change.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another. In this scenario, the metal absorbs heat energy (11 J), which causes its temperature to rise. Understanding how heat transfer works is essential for calculating the specific heat capacity and determining the identity of the metal based on the temperature change observed.

Calculating Specific Heat Capacity

To identify the metal, we can calculate its specific heat capacity using the formula: specific heat capacity = heat absorbed / (mass × temperature change). By substituting the given values (11 J, 4.7 g, and 4.5 °C), we can find the specific heat capacity of the unknown metal and compare it to the known values for titanium and aluminum to make a determination.