In Chapter 17, Scout notices Jem's interest in the case. She isn't sure, at this point, if Jem is being dramatic or if he is really emotionally and intellectually involved in the trial:
Jem’s hand, which was resting on the balcony rail, tightened around it. He drew in his breath suddenly. Glancing below, I saw no corresponding reaction, and wondered if Jem was trying to be dramatic.
As it turns out, Jem is very concerned with the case. Since he is older, he might have a better understanding (than Scout) of the significance of the trial and the potential injustice that would result if Atticus loses the case. He also doesn't want to see his father fail. Jem is quite confident by the end of Chapter 17 when Atticus shows how it was more likely for a left-handed man (Mr. Ewell) to have beaten up Mayella.
Even until the end of Chapter 21, Jem is still very confident. But at the very end of the chapter when the jury gives the guilty verdict, Jem is crushed. Following the trial, Jem continues to try to understand how a jury could make such a poor decision. Atticus tells him, in his own way, how the history of racism led to the unjust verdict.
The one place where a man ought to get a square deal is in a courtroom, be he any color of the rainbow, but people have a way of carrying their resentments right into a jury box. (Chapter 23)