Verbs like eat, drink or smoke often demand a reflexive pronoun to indicate completeness.

Julia ya se ha comido el almuerzo
Julia ya ha comido el almuerzo (sounds extrange, because "el almuerzo" is specific)

Julia ya se comió el almuerzo
Julia ya comió el almuerzo (sounds extrange , because "el almuerzo" is specific)

Julie ya almorzó - Here no specific launch is mentioned. "SE" is nor allowed.

Just to add to Lazarus' post:

If you mean that she has already eaten the food that she brought or bought for her midday meal, I would use either of the following:

Julia ya se ha comido el almuerzo
Julia ya se comió el almuerzo

If you just mean that she has had lunch, I would use this:

Julie ya almorzó

It's a fine distinction, but it's there (at least in English), with one focusing on the food itself, and the other on the action of eating.

Of course, in the right context, you could also just say "Julie ya comió."

Lazarus, I'm hardly the one to pick nits, but "extrange'"

I forgot to mention something very important.
I am trying to stress to the students the difference between possessive adjectives and possessive pronouns.
Does that make a difference in your answers?
Thanks for your help.

Kathleen said:

I forgot to mention something very important. I am trying to stress to the students the difference between possessive adjectives and possessive pronouns.

Does that make a difference in your answers?

Ah. This might not be a good example then, because in Spanish it sounds more natural to say "el almuerzo" than "su almuerzo."

Also, Wikipedia says that possessive adjectives are more properly called possessive pronouns:

"What are traditionally and popularly, if mistakenly, called possessive adjectives ? in linguistic analyses possessive pronouns, possessive determiners or genitive pronouns ? are a part of speech that prototypically modifies a noun by attributing possession to someone or something."

http://en.wikipedia.org/wiki/Possessive_adjective

What exactly are you comparing in Spanish'

Maybe you're looking for something like this?

Julie ya (se) ha comido el suyo.

Vikingo said:

Maybe you're looking for something like this'Julie ya (se) ha comido el suyo.

How about this: Julie has already eaten her lunch, but I'm saving mine for later. Julie se ha almorzado pero, guardo el mio para mas tarde.
Does this make sense for what I'm trying to accomplish'

How about this: Julie has already eaten her lunch, but I'm saving mine for later. Julie se ha almorzado pero, guardo el mio para mas tarde.
Does this make sense for what I'm trying to accomplish'

How about this:

Julie ha lavado su coche, pero no ha lavado el mío.

This way your students can contrast the two types of possessive: su and el mío (her and mine).

Julie ya ha terminado su almuerzo.