One of the benefits of the New Covenant is the placement of the Law within the Believer by writing it on his heart (Jer 31:33; Isa 59:21; Heb 8:10; 10:16). But what is this Law and what does it mean "writing it on his heart"?

For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people. (Jer 31:33, ESV)

And the Holy Spirit also bears witness to us; for after saying,
"This is the covenant that I will make with them
after those days, declares the Lord:
I will put my laws on their hearts,
and write them on their minds," (Heb 10:15-16, ESV)

1. What is the law(s) that the passages above referring to? Aside from the Law of Moses, does God mention any other law?

2. When referring to the heart and mind of a person, the English language sees the term "heart" as the seat of emotion or kindness (i.e. good-hearted, hard-hearted, broken-hearted, etc.), and the term "mind" to represent the seat of thought.

In Hebrew, "heart" has a broader meaning to include the thoughts and logic of a person. It is for this reason that there are no Hebrew terms for the English word "mind." Because the Hebrew definition of heart refers to the heart and mind of a person, it is a term that refers to the essence of a person. To the Jewish audience, how would they understand the above passages?

3. As you keep in mind the benefits of the New Covenant, what observations do you make of the following passages that help you understand God's statement, "I will put my law within them, and I will write it on their hearts?"

Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect. (Rom 12:2, ESV)

But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law. And those who belong to Christ Jesus have crucified the flesh with its passions and desires. (Gal 5:22, ESV)

Do you not know that you are God's temple and that God's Spirit dwells in you? If anyone destroys God's temple, God will destroy him. For God's temple is holy, and you are that temple. (1 Cor 3:16-17, ESV)

Do you not know that your bodies are members of Christ? Shall I then take the members of Christ and make them members of a prostitute? Never! Or do you not know that he who is joined to a prostitute becomes one body with her? For, as it is written, "The two will become one flesh." But he who is joined to the Lord becomes one spirit with him. Flee from sexual immorality. Every other sin a person commits is outside the body, but the sexually immoral person sins against his own body. Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, for you were bought with a price. So glorify God in your body. (1 Cor 5:15-20, ESV)