 Let's go through this problem concerning the heating of air in the lowest part of the atmosphere, which is called the atmospheric boundary. The Sun heats the Earth, and then the Earth heats the air in contact with it. To see how fast the air will heat up, we need to know the heating rate, but we also need to know the air parcel's heat capacity. If the heating rate is given in watts per meter squared, then we can multiply by some arbitrary area to get the total heating rate. Almost always atmospheric heating and cooling occurs at constant pressure. The heat capacity then depends on the specific heat capacity at constant pressure, but it also depends on the air parcel's mass, which is density times volume. So we need to find the density if it isn't given to us. We can use the ideal gas law for that. The volume is just the height times the area, so we put the heating rate on the left-hand side and the effect of the heating on the parcel on the right. We are assuming a fairly uniform air parcel, so we see we really didn't need to multiply by area at all, since it just cancels out. We can rearrange this equation to get the temperature change per time on the left and all the known variables on the right. Then we can put the numbers in and we can find out what the change in temperature with time is.