A metal is thought to be copper or gold. When 18 g of the metal absorbs 58 cal, its temperature rises by 35 °C. (3.6) a. What is the specific heat, in cal/g °C, of the metal?

Verified step by step guidance

1. Identify the formula for specific heat: $c=\frac{q}{m\times \mathrm{\Delta }T}$, where $c$ is the specific heat, $q$ is the heat absorbed, $m$ is the mass, and $\mathrm{\Delta }T$ is the change in temperature.
2. Substitute the given values into the formula: $q=58\text{ cal}$, $m=18\text{ g}$, and $\mathrm{\Delta }T=35\text{ °C}$.
3. Calculate the specific heat using the formula: $c=\frac{58\text{ cal}}{18\text{ g}\times 35\text{ °C}}$.
4. Simplify the expression to find the specific heat in $\text{cal/g °C}$.
5. Compare the calculated specific heat with known values for copper and gold to determine the identity of the metal.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a material-specific property that indicates how much energy a substance can store. The formula to calculate specific heat is given by Q = mcΔT, where Q is the heat absorbed, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, the metal absorbs heat, which causes its temperature to rise. Understanding how heat is transferred is crucial for calculating specific heat, as it directly relates to the energy absorbed by the metal.

Units of Measurement

In this problem, specific heat is measured in calories per gram per degree Celsius (cal/g °C). It is important to be familiar with these units to correctly interpret the results. The mass of the metal is given in grams, and the heat absorbed is in calories, which aligns with the units used in the specific heat formula, ensuring consistency in calculations.