Final answer:
Elizabeth's coldness towards Proctor in Act 2 is due to the strain caused by Proctor's infidelity, leading to a lack of trust and a tense emotional atmosphere.
Step-by-step explanation:
Elizabeth is cold towards Proctor in Act 2 primarily because of the strain in their relationship brought on by Proctor's affair with Abigail Williams. Elizabeth's trust in Proctor has been deeply shaken, leading to a tense atmosphere and emotional distance between them. This cold demeanor reflects the inner turmoil and hurt she feels, while also being indicative of the societal and personal repercussions of Proctor's infidelity within the context of the strict Puritanical setting of the play.