Unified Engineering Thermodynamics Bonus Quiz 2

Fall 2005

NAME SOLUTIONS

1) Frequently we model turbines as being adiabatic and quasi-static and neglect changes in kinetic and potential energy. For such a device operating with air as an ideal gas (R=287 J/kg-K, c_v=716.5 J/kg-K, c_p=1003.5 J/kg-K) which of the following is true?

a) W > W_shaft > 0 > W_flow

b) W_shaft > W > 0 > W_flow

c) W_shaft > W > W_flow > 0

d) W > W_shaft > W_flow > 0

Please support your answer with some analysis.

From the First Law:

and

Thus for the assumptions stated in the problem:

w = Du = - c_vDT and w_s = Dh = - c_pDT . Also, w_f = p₂v₂-p₁v₁ = RT₁ – RT₂ = R(DT).

For a turbine DT < 0. So w_s > w > 0 > w_flow

2) For an aircraft flying at 200m/s, the temperature that the aluminum skin of the aircraft reaches is

a) equal to the temperature of the atmosphere through which it flies

b) less than the temperature of the atmosphere through which it flies

c) greater than the temperature of the atmosphere through which it flies

Why?

Friction between the air and the aluminum skin. Because of viscosity, the aircraft carries with it some of the fluid near to the skin. When viewed from the steady frame of reference of the aircraft, the kinetic energy of the flow is converted into enthalpy when it stagnates on the skin.