If Jesus's death was not eternal, then how can it be substitutionary for the eternal deaths of humans?

As humans, we are under the law. On the day of judgment, everyone will give account of himself. The Greek word for account is logos. It is a log of your disobedience and transgressions, just like the angels in Hebrews 2. It doesn't seem fair to record only your violations, but it is just like your record. You would not expect to find the good things you have done in your police record.

If there is one blemish on your record, the wages is death. Romans 6:23

Jerimiah 17:1 The sin of is written upon the table of your heart. Written in stone, it is your permanent record.

Ezekiel 36:26 I will take away the stony heart out of your flesh, and I will give you a heart of flesh. When we surrender our heart to Jesus, he takes our account (which is in our heart), he puts what is on our account and puts it on his account. He settles our account, gives us a new heart with a fresh account.

Romans 6:7 For sin shall not have dominion over you for you are not under the law, but under grace. What does it mean to not be under the law?

Romans 5:13 sin is not imputed where there is no law. The Greek word for impute is ellogeho. Notice it contains the word log. Impute means to make an entry in the account. Your sin is no longer recorded.

What does it mean to be under grace?

Romans 4:3 Abraham believed God and it was imputed unto him for righteousness. Being under grace, faith-based actions are recorded on our account. Our account is now working in our favor.

Philippians 2:13 For God worketh in you both to will and to do of his good pleasure. When Ephesians 2:8 says it is not about works, it is saying it is not about your works. But it is all about God's works performed in you. That is what is being written on your account.

When you stand before God on THAT day, make sure you are not empty-handed.

N - Assume that the total number of people who will ever live (besides Jesus) is N, a finite number.
ω - Assume that redeeming the smallest sin costs an infinite amount, equal to omega, the hyper-real number.
E - Assume that the most evil person who ever lived committed a number of sins equal to E. Given that our lives are finite, the number of sins that can be committed is finite.
N⋅E⋅ω - Multiply these values together to get the upper limit on the cost of redeeming all the sins of the world. This cost is infinite, but linear in omega.

All Sin ≤ N⋅E⋅ω

Jesus is the "King of kings" and "Lord of Lords". To me, that sounds like at least infinity squared, or ω². Jesus spent between two and three days in the grave (since a part of a day counts as a whole day in Hebrew usage, I am told). Assume the lower figure of two days. That makes Jesus payment equal to 2⋅ω²:

Jesus' Payment = 2⋅ω² >> N⋅E⋅ω ≥ All Sin 

Since Jesus' value is so great, the fact that he only spends a finite amount of time in the grave does not prevent him from making a payment greatly in excess of the cost of our sin. This is because for any finite multiplier M, no matter how big, ω² >> M⋅ω. If this makes no sense, read about how to integrate Greens functions and call me in the morning.

For more on the hyperreal number system and how to perform arithmetic, algebra, limits, integration, and differentiation, see:

https://www.math.wisc.edu/~keisler/calc.html

Admittedly, this is not how most supporters of penal substitutionary atonement would answer, but the important point is that the infinity of our sin is smaller than the infinity of his love, and since we have a well-established mathematical framework for comparing materialistic infinities, there must also be one for comparing spiritual infinities.

As one who believes in the teaching of penal substitution, I would simply point to what the Bible says about it in Romans chapter 5. It would be good if you could read the entire chapter first, in order to grasp the significance of these bits I am going to extrapolate.

Verse 10 - “For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.” Notice how Christ’s death is held in tandem with his life? This is a key point, for if Christ had died and remained dead, there could be no reconciliation of sinners to God. If Jesus’ death had turned out to be eternal, that would have proved that he had died as a sinner and thus his death would have failed to redeem anybody. Only a sinless sacrifice could be acceptable to God.

As Jesus did, indeed, arise from the dead in triumph, that proved him to be the sinless Son of God. The grave can only claim sinners, you see. One who has never sinned lives eternally – unless they voluntarily give over their life to save others, which is what Jesus did. Then the sinless one who dies cannot be held by the grave, which must give the sinless one up.

Then chapter 5 goes on to say how death reigned from Adam onwards, due to all having sinned. That word ‘reigned’ depicts death as a symbolic king ruling over sinners. However, verse 15 shows how death was thrown off its throne!

“But not as the offense, so also the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift of grace by one man, Jesus Christ, hath abounded unto many.”

Something now happens to come to the aid of all men who are all sinners who must die. It is help from above, for helpless sinners can do nothing to escape from their slavery to sin and death. One comes from above, down to where sinners are, and so identifies himself with humanity, he becomes human, yet without sin. Christ was fully human in order to fully represent humanity.

Verses 16 & 17 – “And not as by one who sinned is the gift; for the judgment was by one to condemnation, but the free gift is of many offences unto justification. For if by one man’s offence death reigned by one, much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.”

Adam’s condemnation to all who came from him was sin and death. Jesus Christ’s grace was the gift of righteousness to those receiving that gift. As the passage goes on to show, by the offence of one upon all men came condemnation; but by the one righteousness came justification of life to men. And verse 21 concludes the argument by saying “That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal life by Jesus Christ our Lord.”

The contrast is not Adam’s death with Jesus’ death, but the reign of death overthrown by one righteousness of sinless sacrifice. Sinful death is contrasted with sinless life. That is the substitution! Death has now been substituted by life. Adam’s sin and its resultant death would have carried on ad infinitum had not God sent the sinless Christ into the world to throw death of its throne. Death must have thought it had triumphed supremely when the incarnate Son of God died, until the entrance of Christ into the grave shattered death’s power, once and for all! Death was overcome by the King of Kings and Lord of Lords. The prison gates of death were thrown wide open, for all who would trust only in the triumph of Christ. That is the substitution – not one death for another death, but one sinless death for eternal life, which is why Christ could not be held by death, having conquered it!