Question

How do instant icepacks work in relation to specific heat capacity?

Answer 1

• Minimum temperature reached: Lower for those of higher heat capacity;
• Initial rate of heat exchange: Lower for those of higher heat capacity.

Explanation:

Instant ice packs typically contain water and anhydrous ammonia nitrate `"NH"_4"NO"_3`.[1] The endothermic dissolving of this salt absorbs energy from the surroundings. The exact amount of energy taken in during this process, `Q`, is dependent on

• the number of moles of solid dissolved, and
• the final concentration of the solution.

By the definition of specific heat capacity, the temperature change `Delta T` is inversely related to the standard heat capacity `color(blue)(c)` of the substance if both its mass `m` and the amount of heat transferred `Q` are held constant. That is:

`Delta T=Q/(color(blue)(c)*m)`

Assuming constant initial temperature, a solvent of higher standard heat capacity will lead to a lower `Delta T` hence a less significant drop in temperature.

The rate of heat exchange between two bodies is directly related to the difference in their temperatures.[2]

Thus, increasing the standard heat capacity hence the deviation from the room temperature will speed up heat absorption. As a result, ice packs with larger heat capacity (e.g., containing more water) last longer than those with lower heat capacity- given that they are capable of absorbing the same amount of heat.

References
[1] Wikipedia contributors. "Ice pack." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 18 Apr. 2018. Web. 2 May. 2018.

[2] “Rates of Heat Transfer.” The Physics Classroom, www.physicsclassroom.com/class/thermalP/Lesson-1/Rates-of-Heat-Transfer