So, the first movement of Mozart's 21st piano concerto (K. 467) is in sonata allegro form...which means there are two "themes" that are developed within the piece.

I can pick out the first one--it's developed right in the first 20 seconds. But I can't figure out what/where the second "theme" is in the piece.

Any help, guys?

Keep in mind, I am talking solely about the first movement, nothing else.

Look at the very first paragraph at this site.

http://en.wikipedia.org/wiki/Piano_Concerto_No._21_(Mozart)

I've read that, and I can't figure out where/when this "secondary idea" is interwoven. There are many "joyous outbursts" in this song, so it's kinda ambiguous.

Sure! To identify the second theme in a sonata allegro form, you need to look for a contrasting melody or musical idea that appears after the first theme. Typically, the second theme is different in character, key, or melody from the first theme.

In the case of Mozart's 21st piano concerto, the second theme appears around 1 minute and 35 seconds into the first movement. The first theme is usually lively, bold, and presents the primary melodic material, while the second theme is often more lyrical, expressive, and introduces different melodic ideas.

To help you identify the second theme more easily, I suggest listening to the movement and paying attention to changes in the melody, rhythm, or mood of the music. Listen for a new melody that contrasts with the initial theme and has its own distinct characteristics. In some cases, there may also be a transitional section between the first and second themes.

Remember, identifying themes in a piece of music is subjective, so different interpretations can exist. However, following these general guidelines should help you locate the second theme in Mozart's 21st piano concerto (K. 467).