Can a turbo expander convert more heat to work than a piston expander?

A turbo expander is a turbine moved by high velocity gas hitting it's blades and doing work, reducing it's temperature and pressure. A cylinder-piston expander uses pressurized and/or heated gas to do work on a piston reducing it's temperature and pressure. Let's say in both cases we have the same initial pressure, temperature, and exit pressure. In the case of the turbo, it's pressure and temp is it's stagnation point. The exit velocity is low enough to assume an approximate stagnation condition in both cases.

My question is, in which case can we extract the maximum amount of heat (and do the most amount of work) so that the temperature is lowest for the same exit pressure? So far, in the case of the cylinder-piston expander, the formula for adiabatic expansion seems to give the maximum amount of work that can be done and the lowest temperature that can be reached for a desired exit pressure. If I desired a lower exit temperature, it cannot be done unless I expand to a lower pressure. If I'm mistaken, please correct me.

In the case of the turbo expander, can more work can be done because the heat and pressure can be converted to kinetic energy by increasing the gases' velocity through the nozzle and doing work on the blades? I have yet to work out the formula for that. Any help would be appreciated.

Is this a theoretical question or a practical question?

In theory, if I have gas at temperature T and pressure P going into a black box, with temperature y and pressure p coming out, iit doesn't matter what kind of machinery is in the box - the maximum work is the sane. In practice, it probably depends on more than just piston vs turbine.

Vanadium 50 said:

Is this a theoretical question or a practical question?

In theory, if I have gas at temperature T and pressure P going into a black box, with temperature y and pressure p coming out, iit doesn't matter what kind of machinery is in the box - the maximum work is the sane. In practice, it probably depends on more than just piston vs turbine.

Well it’s both. I’m trying to get the temperature lower at the exit of an expander for a desired pressure. The pressure can’t be lower because it feeds a compressor that has a specific compression ratio. I want to be able to use as much of the added heat to the gas as possible to do work. In the piston case, the heat has caused a rise in pressure which can then be used to do work. In the turbine case the heat has caused an increase in velocity and kinetic energy which can then be used to do work.