An experiment measures the temperature of a 500 g substance while steadily supplying heat to it. FIGURE EX19.20 shows the results of the experiment. What are the heats of fusion and vaporization?

Verified step by step guidance

1. Step 1: Understand the problem. The heat of fusion is the amount of heat required to change a substance from solid to liquid at constant temperature, and the heat of vaporization is the heat required to change a substance from liquid to gas at constant temperature. Both are determined using the heat supplied during the phase transitions, which can be inferred from the graph provided in the experiment.
2. Step 2: Identify the phase transitions in the graph. Look for flat regions in the temperature vs. heat graph where the temperature remains constant while heat is being supplied. These regions correspond to the phase transitions: solid to liquid (fusion) and liquid to gas (vaporization).
3. Step 3: Calculate the heat of fusion. Use the formula \( Q = m \cdot L_f \), where \( Q \) is the heat supplied during the fusion phase (determined from the graph), \( m \) is the mass of the substance (500 g or 0.5 kg), and \( L_f \) is the latent heat of fusion. Rearrange the formula to solve for \( L_f \): \( L_f = \frac{Q}{m} \).
4. Step 4: Calculate the heat of vaporization. Use the formula \( Q = m \cdot L_v \), where \( Q \) is the heat supplied during the vaporization phase (determined from the graph), \( m \) is the mass of the substance (500 g or 0.5 kg), and \( L_v \) is the latent heat of vaporization. Rearrange the formula to solve for \( L_v \): \( L_v = \frac{Q}{m} \).
5. Step 5: Interpret the results. Once the values of \( Q \) for fusion and vaporization are identified from the graph, substitute them into the respective formulas to calculate \( L_f \) and \( L_v \). These values represent the heats of fusion and vaporization for the substance.

Key Concepts

Heat of Fusion

The heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point, without changing its temperature. This process involves breaking the intermolecular forces that hold the solid structure together. For example, when ice melts to water, it absorbs heat equal to its heat of fusion, allowing the phase change to occur.

Heat of Vaporization

The heat of vaporization is the energy needed to convert a liquid into a gas at its boiling point, again without a change in temperature. This energy is used to overcome the attractive forces between the molecules in the liquid phase. For instance, when water boils and turns into steam, it requires a specific amount of heat equal to its heat of vaporization to facilitate this transition.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a crucial concept in thermodynamics, as it determines how much energy is needed to change the temperature of a substance. In the context of the experiment, understanding specific heat capacity helps in calculating the heat supplied to the substance as its temperature changes before phase transitions occur.