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Difficulty: HardThermodynamics and Heat

Two solid samples of equal mass, Substance A and Substance B, are heated in separate insulated containers at the exact same constant rate. During the heating process, Substance A exhibits a much steeper rate of temperature increase prior to melting, but requires three times as much time to fully melt at its melting point compared to Substance B. Which of the following conclusions correctly compares the thermal properties of Substance A to Substance B?

  1. A
    Substance A has a higher specific heat capacity and a lower latent heat of fusion than Substance B.
  2. Substance A has a lower specific heat capacity and a higher latent heat of fusion than Substance B.Answer
  3. C
    Substance A has a higher specific heat capacity and a higher latent heat of fusion than Substance B.
  4. D
    Substance A has a lower specific heat capacity and a lower latent heat of fusion than Substance B.

Answer

Substance A has a lower specific heat capacity and a higher latent heat of fusion than Substance B.
Specific heat capacity (cc) measures the thermal energy required to raise the temperature of a given mass (Q=mcΔTQ = mc\Delta T). Under identical mass and heat supply, a steeper slope (faster temperature rise) signifies a lower specific heat capacity. Latent heat of fusion (LfL_f) governs the energy absorbed at a constant temperature during melting (Q=mLfQ = mL_f). A longer duration spent in the solid-to-liquid plateau indicates that a greater amount of energy was required to completely melt the sample, proving Substance A has a higher latent heat of fusion.

Step-by-Step Solution

1
Analyze the rate of temperature rise before phase change in relation to specific heat capacity.
The rate of temperature increase is inversely proportional to specific heat capacity (c=QmΔTc = \frac{Q}{m \Delta T}). Because both samples have identical mass and heat input rates, a steeper temperature increase means Substance A requires less energy per degree change, indicating a lower specific heat capacity.
Specific heat capacity defines the amount of thermal energy required to raise the temperature of a unit mass by one degree.
2
Analyze the duration of the melting phase transition in relation to latent heat of fusion.
The energy absorbed during melting at constant temperature is given by Q=mLfQ = m L_f. Because the heating rate is constant, taking three times as long to melt means Substance A absorbs three times more energy during phase change, indicating a higher latent heat of fusion.
Latent heat of fusion defines the energy required to change a substance from solid to liquid at its melting point without a change in temperature.
3
Combine the deduced properties to determine the correct relationship.
Substance A possesses a lower specific heat capacity and a higher latent heat of fusion compared to Substance B.
Synthesizes the solid-state heating behavior and the isothermal phase transition behavior.

Key Concept

Relationship between heating curve slopes, specific heat capacity, and latent heat of fusion
Estimated Time:1m 30s
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Topics

Thermodynamics and Heat

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