Why does an air parcel cools as it rises

That force is 'gravity'. Gravity's role is its pull of cooler, denser air toward the earth's surface. As the denser air reaches the earth's surface it spreads and undercuts the less dense air which, in turn, forces the less dense air into motion causing it to rise. This is how hot air ballooning works.

A flame is used to heat the air inside of the balloon making it less dense. Outside of the balloon, the cooler, denser air is pulled down by gravity. The cooler air undercuts the warmer, less dense air trapped inside the balloon causing it to lift.

This is why thunderstorms often form along weather fronts. A front represents the boundary where cooler, more dense air undercuts less dense, warmer air forcing it up into the atmosphere forming the storms.

In meteorology, we often treat 'pockets of air' in a similar way to ballooning. We call these pockets of air "parcels". As a result, condensation releases latent heat, which heats the plot, which cools less than expected by the dry adiabatic. The plot follows the blue curve of the figure, called wet adiabatic. The temperature profile in the immediate environment may be such that the air parcel, when it exceeds a certain altitude, becomes warmer than its environment. This ascent continues until the parcel becomes colder than its surroundings, at an altitude called the E quilibrium Temperature Level ETL.

The parcel then slows down and eventually stops. The larger the CAPE, the faster the air parcel rises. This is the energy required to force the air parcel up to its free convection level. Because the dew point temperature keeps track of the amount of water vapor in the parcel, it must decrease once a cloud begins to form by condensation water vapor condensing to the tiny liquid droplets that make up a cloud. The decrease in the dew point temperature indicates that there is a decreasing amount of water vapor in the air parcel.

The water does not disappear though, it is condensing into the liquid that is the cloud. Now lets look at another numerical example. Below is a link to two tables. The first table shows you what you would know about the atmosphere before performing lifting a surface parcel upward. You would have to determine at what altitude a cloud would form by filling in the blanks.

The second table shows the solution. NOTE: Please do not worry about the columns labeled environmental temperature and stability, we have not covered that material yet. You will be expected to do similar examples in homeork. Click Here to view the example. Although the instructive method of filling in a table to keep track of what happens to air parcels as they rise is somewhat simplified, I believe it is very helpful in getting a first-order understanding of how clouds form.

You will have to perform similar exercises in both homework problems and exams, so you should understand how to do it and the reasoning behind the rules for doing it.