The air temperature above coastal areas is profoundly infuenced by the large specific heat of water. One reason is that the energy released when `1m^3` of water cools by `1^@C` will raise the temperature of a much larger volume of air by `1^@C`. Find this volume of air. The specific heat of air is approzimately `1 kJ//kg^@C`. Take the density of air to be `1.3 kg//m^3`.

The air temperature above coastal areas is profoundly infuenced by the

1.	The air temperature above coastal areas is profoundly infuenced by the large specific heat of water. One reason is that the energy released when `1m^3` of water cools by `1^@C` will raise the temperature of a much larger volume of air by `1^@C`. Find this volume of air. The specific heat of air is approzimately `1 kJ//kg^@C`. Take the density of air to be `1.3 kg//m^3`.
Answer» The mass of `1m^3` of water is specified by its density, `m=rhoV=(1.00xx10^3 kg//m^(3)))(1m^3)=1xx10^3kg` When `1m^3` of water cools by `1^@C`, it releases energy `Q_c=mcDeltaT=(1xx10^3kg)4186 J//kg.^@C(-1^@C)=-4xx10^6J` Where the negative sign represents heat output. When `+4xx10^6J` is transferred to the air, raising its temperature by `1^@C`, the volume of the air is given by `Q_c=mcDeltaT=rhoVcDeltaT` `V=(Q_c)/(rhocDeltaT)=(4xx10^6J)/((1.3kg//m^3)(1xx10^3J//kg^@C)(1^@C))=3xx10^3m^2` The volume of the air is a thousand times larger than the volume of the water.

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