Problem: Suppose you are cold-weather camping and decide to heat some objects to bring into your sleeping bag for added warmth. You place a large water jug and a rock of equal mass near the fire. Over time, both the rock and the water jug warm to about 38 oC (100 oF). If you could bring only one into your sleeping bag, which one should you choose to keep you the warmest?

🤓 Based on our data, we think this question is relevant for Professor Blake's class at UCI.

FREE Expert Solution

Recall:

$\boxed{\mathbf{q}\mathbf{=}\mathbf{mc}\mathbf{∆}\mathbf{T}}$

where m = mass in g

            c = heat capacity in J/g°C

            ΔT = change in temperature

Isolating c (heat capacity):

$$\begin{gathered} \frac{\mathbf{q}}{\mathbf{m}\mathbf{∆}\mathbf{T}}\mathbf{=}\frac{\cancel{\mathbf{m}}\mathbf{c}\cancel{\mathbf{∆}\mathbf{T}}}{\cancel{\mathbf{m}\mathbf{∆}\mathbf{T}}} \\ \boxed{\mathbf{c}\mathbf{=}\frac{\mathbf{q}}{\mathbf{m}\mathbf{∆}\mathbf{T}}} \end{gathered}$$

The heat capacity of water is 4.186 J/g°C. 

An average rock has a heat capacity of 2.0 J/g°C.