Why does Carton die with a noticeably peaceful face

Fortunately, Carton acts as a deus ex machina (a god-like intervention), arriving on the scene and instantly working to save Darnay's life. As we can see, he is a changed man. He longer hides from the world in liquor; instead, he uses it to find all sorts of information about the world. He no longer tolerates being spoken at; he loudly and forcefully orders Barsad around. Finally, he no longer speaks as a wastrel, but as a man with a purpose. He uses the last vestiges of his old life to provide information for his purpose through likening his questioning to the rake's game of cards. Carton goes to the guillotine with a peaceful, philosophical face. He dies with the conclusion that "It is a far, far better thing that I do than I have ever done; it is a far, far better rest that I go to than I have ever known."

Fortunately, Carton acts as a deus ex machina (a god-like intervention), arriving on the scene and instantly working to save Darnay's life. As we can see, he is a changed man. He longer hides from the world in liquor; instead, he uses it to find all sorts of information about the world. He no longer tolerates being spoken at; he loudly and forcefully orders Barsad around. Finally, he no longer speaks as a wastrel, but as a man with a purpose. He uses the last vestiges of his old life to provide information for his purpose through likening his questioning to the rake's game of cards. Carton goes to the guillotine with a peaceful, philosophical face. He dies with the conclusion that "It is a far, far better thing that I do than I have ever done; it is a far, far better rest that I go to than I have ever known."