Question: Kelim of Nochrim should not need to be Kashered for use after that day!

Answer: Chachamim decreed to Kasher them, lest they be used the same day.

The opinion that forbids Nosen Ta'am li'Fgam holds that even absorptions in a Ben Yomo are slightly Pagum (therefore, we do not distinguish. All absorptions are forbidden, even after 24 hours, when they are very Pagum.)

(Our Mishnah): A roasting spit or grill (of a Nochri) is Kashered through Libun;

Contradiction (Rav Amram - Mishnah): A roasting spit or grill (on which Kodshim were cooked) is Kashered through Hag'alah in hot water.

Answer #1 (Rav Sheshes): Kodshim Kelim are more lenient because they absorbed permitted taste. Nochri Kelim absorbed forbidden taste.

Objection (Rabah): What difference does it make? In both cases, they emit forbidden taste! (After a day or two, Kodshim are Asur due to Nosar.)

Answer #2 (Rabah): When the Mishnah says that Hag'alah is required for Kodshim Kelim, this means Shetifah u'Merikah (rinsing and scouring, in the Azarah, just like one must launder a garment that absorbed blood of a Chatas in the Azarah. However, Kashering is only through Libun.)

Objection (Abaye): Shetifah u'Merikah is with cold water. The Mishnah specifies Hag'alah, which is in hot water!

Answer #3 (Abaye): Each Mishnah teaches about the other:

Our Mishnah teaches that Nochri Kelim require Libun. The same applies to Kodshim Kelim;

That Mishnah teaches that Kodshim Kelim require Hag'alah. The same applies to Nochri Kelim.

Objection (Rava): If so, one of the Mishnayos should have taught Libun and Hag'alah, and the other should teach one of these methods, and we would learn the other method from the other Mishnah!

Answer #4 (Rava): Kodshim Kelim do not require Libun due to Rav Nachman's reasoning;

(Rav Nachman): Cooking Kodshim in a pot purges the pot from absorptions of the previous day's Kodshim (before they become forbidden).

Question: This applies only to Shelamim (which may be eaten for two days), for today's absorptions are still permitted when cooking in it tomorrow;

However, if Chatas is cooked today, one may cook in it tomorrow (for it will emit absorptions of today's Chatas, which will be forbidden)!

Answer: After cooking Chatas, one cooks Shelamim that same day (to purge the pot from absorbed Chatas). The absorptions of Shelamim will be purged tomorrow.

Objection: If so, Kodshim Kelim should not even need Hag'alah!

This is left difficult.

Answer #5 (Rav Papa): Nochrim do not constantly cook in their Kelim, so the absorptions become hard, and Libun is required. Kodshim Kelim are used constantly, so the absorptions never become hard, and Hag'alah suffices.

Defense of Answer #1 (Rav Ashi): Kodshim Kelim are more lenient because they absorbed permitted taste;

Objection (Rabah): In both cases, they emit forbidden taste!

Answer (Rav Ashi): Genuine Isur never touched Kodshim Kelim, just the absorptions became Nosar.

Question: What level of Libun is required?

Answer (Rav Mani): One must heat them until the surface peels off.

Question: How is Hag'alah of Kelim done?

Answer (Rav Huna): A small pot is put in a bigger pot (of boiling water).

Question: How is Hag'alah done for a big pot?

Answer: Rav Ukva had a big pot to Kasher. He put dough around the brim, filled it with water up to the brim, and boiled the water.

Rava: Rav Ukva is a great Chacham. He knows that this suffices!

When Isur was cooked in the pot, sometimes (boiling) drops would splash on top of the brim. We purge the absorptions (Kasher it) the same way they were absorbed. It suffices that such drops splash on the brim.

(Mishnah): A knife is Kashered by rubbing it on a sharpening stone.

(Rav Ukva bar Chama): Also, he must (Rashi; Ramban - alternatively, he may) insert it 10 times in the ground

(Rav Huna brei d'Rav Yehoshua): He must insert it in virgin soil.

(Rav Kahana): This refers to a knife without crevices.

Support (Beraisa): A knife without crevices may be Kashered by inserting it 10 times in the ground.

(Rav Huna brei d'Rav Yehoshua): This suffices to use for cold food.

Mar Yehudah and Bati bar Tuvi were eating with Shevor Malka (a Nochri). Shevor Malka cut an Esrog and gave some to Bati bar Tuvi. He inserted the knife 10 times in the ground, cut a piece and gave it to Mar Yehudah.

Bati bar Tuvi: You Kashered it for him because he is a Yisrael. You do not consider me to be a Yisrael?!

Version #1 - Shevor Malka: I know that he would not eat unless I did so. I did not know that you are so particular.

Version #2 - Shevor Malka: Remember what you did last night! (Rashi - Persian women were offered to Bati and Yehudah. Bati accepted, and Yehudah refused. Tosfos - slaves were offered to them. Bati accepted because he was a slave.)