A differential scanning calorimetry $\text{(DSC)}$ experiment tracks the heat flow into or out of a system as a function of temperature. If the experiments given in the options below are performed at 1 atmospheric pressure, then in which case will the DSC thermogram exhibit a spike, either upward or downward?
- Heating $10$ mg of pure Cu from $323 \mathrm{~K}$ to $673 \mathrm{~K}$
- Cooling pure water from $323 \mathrm{~K}$ to $278 \mathrm{~K}$
- Heating pure ice from $263 \mathrm{~K}$ to $284 \mathrm{~K}$
- Cooling a Pb-Sn alloy at the eutectic composition from $323 \mathrm{~K}$ to $273 \mathrm{~K}$
