Question

A 10 m3rigid insulated tank contains air at 1000 kPa, 1000 K. It is connected to an adiabatic reversible turbine that has an exit of 100 kPa.

The air is now allowed to run out through the turbine until a tank pressure of 100 kPais reached and the flow stops.

a) Find the initial and final mass in the tank.

b) How much work did the turbine produce.

Answer 1

a) initial mass = 34.85 gm, final mass = 3.48gm

b)

Step-by-step explanation:

At the initial state, the:

Pressure, p1 = 1000kPa,

Temperature, T1 = 1000K,

Volume, V1 = 10 m³

The mass of air in the tank can be evaluated using;

m1 = (p1 x V1) /(R x T1)

m1 = (1000 x 10)/(287 x 1000)

Therefore, m1 = 34.85g

At the final state,

Pressure, p2 = 100kPa,

Temperature, T2 = 1000K,

Volume, V2 = 10 m³

The mass of air in the tank is given by;

m2 = (p2 x V2) / R x T2

m2 = (100 x 10)/ 287 x 1000

Therefore m2 = 3.48 gm