Question

In class we considered the situation of a parcel being warmed isobarically from below by a large thermal reservoir. The parcel has temperature Tp initially and the surface has temperature Ts. We assumed that Ts does not change appreciably if the surface is large compared to the parcel. Please show that this is true for liquid water warming air: Assume that 1 cm^3 of liquid is warming a 1 cm^3 parcel of air that is directly above it. If the parcel temperature rises by 1 K, how much does the water cool?

Answer 1

The specific heat capacity of water is, 4200 J/kg. The specific heat capacity of air is 1000 J/kg. The densities of water and air are 1000 kg/m^3 and 1.225 kg/m^3 respectively.

Therefore the mass of air having volume 1 cm^3 is given by,

To change the temperature of air by 1 K, we get the amount of heat energy as,

This energy is lost from water.

Mass of water having volume 1 cm^3 is given by,

Hence we can calculate the change in temperature of water as,

You can see the change in temperature is very small to the change in temperature of air.