Problem — Temperature and heat

Problem

A pot contains $1$ kg of water at $80\,^{\circ}$C; a swimming pool contains $10^4$ kg of water at $25\,^{\circ}$C. Which of the two contains more thermal energy? Which “burns” more if you put a finger in it? Explain in five lines the difference between temperature and energy.

A small pot of boiling water next to a large swimming pool of lukewarm water.

Solution

The stored thermal energy is proportional to the product $m \cdot c \cdot T$ (mass, specific heat and absolute temperature).

For the swimming pool, the enormous mass dominates: $E_{\text{piscina}} \approx 10^4 \cdot 4186 \cdot 298 \approx 1{,}2 \cdot 10^{10} \ \text{J}$

much larger than for the pot: $E_{\text{pentola}} \approx 1 \cdot 4186 \cdot 353 \approx 1{,}5 \cdot 10^{6} \ \text{J}$

So the swimming pool contains much more total thermal energy. Whether it “burns” the finger, however, depends on temperature: it is the temperature difference between the water and the skin that determines the heat flow into the finger. The pot at $80\,^{\circ}$C burns, the pool at $25\,^{\circ}$C does not. Temperature measures the intensity of thermal agitation (the average energy per molecule), while total thermal energy also depends on mass: they are two different quantities.

$\ev{\text{Pool: more total energy} \qquad \text{Pot: burns more}}$

Collegamenti

Argomenti: Termologia Concetti: Calore specifico e capacità termica · Temperatura