When 100 cal (418 J) of heat is applied to a 125 g sample, the temperature increases by 28 °C. Calculate the specific heat of the sample and compare your answer to the values in Table 1.10. What is the identity of the sample?

Verified step by step guidance

1. Step 1: Recall the formula for specific heat capacity: $c\; =\frac{q}{m\mathrm{\Delta T}}$, where $q$ is the heat energy applied, $m$ is the mass of the sample, and $\Delta T$ is the change in temperature.
2. Step 2: Identify the given values from the problem: $q\; =\; 418\; \backslash ,\; J$, $m\; =\; 125\; \backslash ,\; g$, and $\Delta T\; =\; 28\; \backslash ,\; ^\{\backslash circ\}C$.
3. Step 3: Substitute the given values into the formula: $c\; =\frac{418}{12528}$. Perform the division in the denominator first, then divide $418$ by the result.
4. Step 4: Compare the calculated specific heat value to the values in Table 1.10. Look for a material with a specific heat value close to your result to identify the sample.
5. Step 5: Conclude the identity of the sample based on the comparison. For example, if the specific heat matches that of aluminum, the sample is likely aluminum.

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 helps in understanding how different substances respond to heat. The formula to calculate specific heat (c) is c = Q / (m * ΔT), where Q is the heat added, m is the mass, 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, heat is applied to the sample, causing its temperature to rise. Understanding the principles of heat transfer is essential for calculating specific heat and analyzing thermal properties of materials.

Material Identification

Material identification involves comparing the calculated specific heat of a sample with known values in reference tables. Each substance has a characteristic specific heat, which can be used to identify it. By determining the specific heat from the experiment and comparing it to standard values, one can infer the identity of the material in question.