Question

fall final exam: mc
a solid melts (gains energy) in a constant - table until it reaches its liquid phase. the specific heat capacity in the solid phase is greater than in the liquid phase.
which graph shows how the temperature of the mass varies with time?
(there are four graphs labeled a, b, c, d with temperature on the x - axis and time on the y - axis, and multiple - choice options a, b, c, d are provided.)

Explanation:

To determine the correct graph for a solid melting into liquid (with solid - liquid phase change), we recall the heating - cooling curve concepts:

1. Phase Change Region: During the phase change (melting), the temperature remains constant while heat is absorbed (latent heat of fusion). So, the graph should have a horizontal segment (constant temperature) when the phase change occurs.
2. Specific Heat Capacity: The problem states that the specific heat capacity in the solid phase is greater than in the liquid phase. The slope of the temperature - time graph (where time is related to heat input) is given by $\frac{\Delta T}{Q}=\frac{1}{mc}$, so a smaller specific heat capacity ($c$) leads to a steeper slope (since $m$ is constant for the same mass of the substance). In the liquid phase, with smaller $c$, the slope should be steeper than in the solid phase.
3. Analyzing the Graphs:

• Graph A: It shows a decrease in temperature (cooling), but we need heating (melting is heating a solid to liquid), so A is incorrect.
• Graph B: It has a horizontal segment (phase change) and the slope of the liquid part (after phase change) is steeper than the solid part (before phase change), which is consistent with $c_{solid}>c_{liquid}$.
• Graph C: It is a curve, which is not typical for a heating curve with a phase change (heating curves with phase changes have linear segments with different slopes and a horizontal segment for phase change).
• Graph D: It has no horizontal segment for the phase change, so it does not represent a phase change process correctly.

Answer:

B