Thomas Aquinas

“ For the atonement by which one satisfies for self or another is called the price, by which he ransoms himself or someone else from sin and its penalty, according to Dan. 4:24: "Redeem thou thy sins with alms." Now Christ made satisfaction, not by giving money or anything of the sort, but by bestowing what was of greatest price---Himself---for us. And therefore Christ's Passion is called our redemption.
Reply to Objection 1: Man is said to belong to God in two ways. ”

“ But since Christ's humanity is the "instrument of the Godhead," as stated above ( [4258] Q [43] , A [2] ) , therefore all Christ's actions and sufferings operate instrumentally in virtue of His Godhead for the salvation of men. Consequently, then, Christ's Passion accomplishes man's salvation efficiently.
Reply to Objection 1: Christ's Passion in relation to His flesh is consistent with the infirmity which He took upon Himself, but in relation to the Godhead it draws infinite might from It, according to 1 Cor. 1:25: "The weakness of God is stronger than men" ”

“ Further, it does not seem to be consistent for the same agent to operate by way of merit and by way of efficiency, since he who merits awaits the result from someone else. But it was by way of merit that Christ's Passion accomplished our salvation. ”

“ Although the truth answers to the figure in some respects, yet it does not in all, since the truth must go beyond the figure. Therefore the figure of this sacrifice, in which Christ's flesh is offered, was flesh right fittingly, not the flesh of men, but of animals, as denoting Christ's. ”

“ But he has not paid who has not fully atoned. Therefore it appears that Christ by His suffering has fully atoned for our sins.
I answer that, He properly atones for an offense who offers something which the offended one loves equally, or even more than he detested the offense. ”