What JDE said is correct, although I didn't take the time to double-check his math.

Let me make this more complicated. For an adiabatic (meaning no heat transfer), isentropic (meaning 100% efficient) compression process, the equation for "power" (assuming air is an ideal gas) is:

POWER = { mdot * k * R * T1 * [1 - (P2/P1)^((k-1)/k)] } / { 1 - k }

(wow!)

where,

POWER = shaft horsepower required, in kJ/sec.

mdot = mass flow rate of air (in kg/sec)

k = ratio of specific heats for air (around 1.395 for air in the temperature ranges we're talking about)

R = the universal gas constant for air (0.287 kJ/kg-K)

T1 = the air inlet temperature to the compressor (in degrees K)

P2/P1 = the pressure ratio for the turbo outlet to inlet (in absolute, not gauge, pressures)

When you're all done, you have the 100%-efficiency power required to compress the inlet air. If you then devide by the compressor efficiency, you get the actual power required.

Here's an example, from my car: about 300 grams/sec (0.3 kg/sec) mass air flow, 20 psi of boost, 60 degree F air coming into the turbo. Let's say the compressor efficiency is around 70%.

P2/P1 = (20+14.7psi) / (14.7 psi) = 2.36 (remember, absolute pressures, not gauge pressures)

T1 = 60 deg. F = 289 Kelvin (K)

POWER = { 0.3kg/s * 1.395 * 0.287kJ/kg-K * 289K * [1-(2.36^0.283)] } / { 1 - 1.395 }

POWER = 24.17 kJ/sec, if the compressor is 100% efficient. For a 70% efficient compressor:

ACTUAL POWER = POWER / EFFICIENCY = 24.17kJ/sec / 0.7 = 34.53 kJ/sec, which converts to 46.3hp (1 hp = 0.746kJ/sec). That's for my typical low-12/high-11 second car. For faster cars, the power required to drive the compressor will go up dramatically, since "mdot" will be a lot higher.

See, it's easy! (Kids, don't try this at home).

You can use the exact same equations to estimate how much CO2 ("mdot") you would need to produce the 34.53kJ/sec that the compressor needs. For CO2, your values for "k" will be around 1.26, "R" will be 0.189 kJ/kg, and your "T1" will be whatever temperature the CO2 is leaving the bottle at. You will have to guess what your "P2/P1" and your turbine efficiency are.

One other thing - metals can do some goofy things at very low temperatures. When you start injecting CO2 at very low temperatures into a turbine that's designed for high temperatures, internal metal stresses and clearances are going to be a lot different than what they were designed for. It wouldn't surprise me if turbing housings and blades started to crack at those ultra-low temperatures. Something to consider.

Good Luck,