# Thermodynamics turbocharger question

## Homework Statement

A 10 L truck engine has a volumetric efficiency of 100%. It has a turbocharger which increased the mass flow of air and its pressure by a factor of 2 when the engine is running at 4300 rpm. Find the turbocharger rpm, efficiency, and the temperature of the air leaving the turbo.

Inlet conditions are 1 atm and 80 degrees F. The AFR is 98% and therefore the volume occupied by fuel is negligible. Also, the turbocharger can be assumed to be adiabatic

(Also given compressor map not shown here)

The attempt at a solution
So I first used the ideal gas law to find the density of air at the given conditions. Using this density, I then used the volumetric equation to find the mass flow rate through the turbo, and doubled that value since it is increased by a factor of two. Now by looking at the compressor map, I have the corrected air flow, as well as the pressure ratio, which allowed me to find the rpm as well as the compressor efficiency. This is where I got stuck. Assuming an isentropic turbo, I was able to find the ideal exiting temperature of the air using the T2 = T1(P2/P1)^(k-1/k) equation. Using that value, I then plugged it back into the efficiency equation and found the actual exiting temperature of the air. Now I have the inlet and outlet temps of the air in the compressor, as well as the turbo rpm speed, but know nothing about the turbine efficiency or temperatures. Is there a relationship between the turbine and compressor that I am missing? Or is there another way to find the temperature of the turbine?

I am assuming that I need to find the outlet temperature of the turbine, and then go about finding the efficiency of the turbine. With the efficiency of the compressor and the turbine, I can then find the efficiency of the whole turbocharger. I am just not seeing how to find any information on just the turbine.

Any help?