At face value this is incredibly simple. What is the temp pre/post turbo. That's the temperature delta.
Am I missing what you're asking?
-Wait, you asking hypothetical, not actual? You're not running 36PSI currently? Oh, you need to calcualted temperature to size an aftercooler. I thought this was all running in your car.
Use PV=NRT (Ideal Gas Law).
https://en.wikipedia.org/wiki/Ideal_gas_law
You should be able to calculate the temperature differential based on compression. Compress gas "X" to 35 PSI equates to a rise of "Y" thermal units provided the volume remains constant. This in turn can be converted into BPU from the temperature. IF you're really concerned you also should take a look at gas velocity pre/post IC based on heat loss. Also, if the chamber is large enough and the deltas are great enough, you could run into condensation and such in/post aftercooler.
I mean the ideal gas law helps to an extent but this is more of a thermodynamics question, meaning he’d want Q=McAt
It’s a question of specific heat capacity, he wants to know how much water he’d need to keep the delta in temperature as little as possible.
Now, the ideal gas law **should** give you an idea of what your initial temperature would be prior to the charge air hitting the intercooler, however if there is a temp sensor there, that would be ideal data to use rather than a rough calculation. Not to mention, PV=nRT would be hard to use because our volume is changing depending on both on the phase of the crankshaft and on whatever the diverter valve or wastegate are doing. Those factors would make that a much more complex way of calculating the temperature, and thus the heat he needs to remove from the charge air. Not to mention, the n component of the ideal gas law would be difficult to pin down accurately unless all of your other variables are given, and we’ve already sort of discussed how they aren’t.
So, specific heat capacity of water (at 1 atm and 20 degrees Celsius) is about 4.182 Joules/(gram*degree Celsius) so your essentially trying to find the mass (and therefore the quantity) of water necessary to absorb the heat given off, and you’d then have to have a heat exchanger that could take that heat energy and radiate it, which is gonna be another Q=mcAt equation.
Essentially, what OP wants is to calculate the heat (Q) of the charge air, use that value of Q to calculate the mass (m) of water that would be required to absorb the heat and then they’d need to determine how much heat (Q) the heat exchanger/radiator portion of his proposed aux cooling system would need to radiate so as to cool the water off well enough.
The latchkey here is the heat exchanger that will be radiating the heat from the water out into the air. Even with a ton of water (which gets heavy quickly) without an efficient enough exchanger your just going to delay heat soak rather than prevent it. It’s entirely possible, with a solid radiator that sees airflow and a strong pump that the actual quantity of water necessary to achieve the stated goal would be relatively small.
But yeah, to answer the original question, the first law of thermodynamics would be your friend. The problem lies in what is determined to be an ‘adequate’ heat sink. Most radiators are gonna be entirely dependent on the airflow they receive, assuming the new water jacket intercooler would be mounted elsewhere in the engine bay you could theoretically place the radiator(s?) for the separate cooling circuit where the front mount intercooler go, but again this would be a really complex fix for something that can be handled pretty well by a standard air to air intercooler.
