1. Consider the steady state, one-dimensional, adiabatic flow of an ideal gas in a passage

of variable area. Suppose that the gas emerges from a chamber at temperature To with

negligible kinetic energy and is accelerated to a velocity V in a passage of appropriate

design. At this point it has temperature T, sound speed a, and Mach number M = = V/a.

For the ideal gas, a² = RT. Show that

To

T

= 1+

2

M².

2. Oxygen enters a turbine at 200 K and 60 atm. The turbine discharges into a separator,

from which saturated liquid and saturated vapor emerge at 1 atm as separate streams.

The system is perfectly insulated. The turbine shaft-power output is 1700 W, and the

total oxygen flow rate is 15 kg/s. What is the net liquid-oxygen mass flow rate?