Joon Seong Tan has pleaded not guilty to killing Ms Zhang in February 2021, a month after they started dating.
After being interviewed by police about her disappearance, Tan allegedly searched online for the phrase "how many years for killing a person in Australia".
He also allegedly searched for "how is stinky garbage disposed in Australia" and "garbage disposal in Australia".
It's alleged Tan murdered Ms Zhang in her home sometime between 5pm and 6pm on February 2, 2021 after sharing dinner with her and her eight-year-old son.
Ms Zhang had reportedly soured on the relationship with Tan and had started seeing another man, Tzu-Hao 'Eric' Hung.
Mr Hung told the jury on Tuesday that he met Ms Zhang online after she posted about wanting to make new friends.
They began speaking over WeChat and she invited him to play cards with her and her friend Xiaolei 'Shelly' Chi.
Ms Chi and Ms Zhang were close friends and spoke on the phone as often as four or five times a day, she told jurors.
But while Ms Zhang was moving on, Tan allegedly remained keen on her and referred to her as his "wife" in conversations with friends, prosecutor Jeremy McWilliam told jurors.
Tan allegedly told a friend he believed Ms Zhang was cheating on him and if he found out that was the case he would "kill her, hug her and die together".
Mr McWilliam said Ms Zhang was subjected to a sustained and deliberate assault with at least one stab wound to her heart.
It's alleged Tan asked a friend to come to Ms Zhang's house, where he said they had fought and he killed her accidentally before cleaning up and moving her body to a laundry cupboard.
He then allegedly moved her body into a wheelie bin, drove it to Heidelberg West and placed it with others out for collection.
The following morning, after driving Ms Zhang's son to school, he allegedly returned and watched the garbage truck empty the bin, before returning it to Ms Zhang's home.
Ms Zhang's body was discovered by police during a search of a Wollert landfill site in June 2021.
Tan was arrested at Melbourne Airport on February 10, 2021. The trial is continuing.
