Problem — Air with doubled c

Problem

Imagine the specific heat of air suddenly doubled, $c'_{\text{aria}} = 2010$ J/(kg$\cdot$K) instead of about $1005$. Discuss in five lines the impact on: (a) the daily temperature swing of the climate; (b) the heating time of a room; (c) the overall heat loss.

Solution

Doubling the specific heat $c$ means twice the energy is needed to change the same mass of air by $1\,^{\circ}$C. (a) Climate: the temperature swings between day and night would halve and temperatures would be more stable, because the air would absorb more heat before warming up (and release more before cooling down). (b) Heating a room: with the same boiler it would take roughly twice as long (or twice the power) to bring the air to the desired temperature. (c) Heat loss: at steady state, heat loss depends mostly on conduction and insulation rather than on $c$, but the air would store more energy, making rooms thermally more inert and better able to retain heat. In short, air with double the specific heat would give a milder, more stable climate, but slower heating.

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Topics: Termologia Concepts: Calore specifico e capacità termica