Question

Oxygen enters an insulated 12-cm-diameter pipe with a velocity of 70 m/s. At the pipe entrance, the oxygen is at 240 kPa and 20°C, and at the exit it is at 200 kPa and 18°C. Calculate the rate at which entropy is generated in the pipe.

Answer 1

S = 0.10253 kW/k

Step-by-step explanation:

Given data:

Velocity of oxygen ( V ) = 70 m/s

Diameter of pipe = 12-cm = 0.12 m

At entrance

pressure of oxygen ( p1 ) = 240 kPa

Temperature of oxygen ( T1 ) = 20°c = 293 k

At exit

pressure of oxygen ( p2 ) = 200 kPa

temperature of oxygen ( T2 ) = 18°c = 291 k

First calculate specific volume of oxygen at inlet

V1 =
`(RT1)/(P1)` -------- ( 1 )

R = 0.2598 KJ/kgk ( property of oxygen )

T1 = 293 k

P1 = 240 kpa

substitute values into equation 1

V1 = 0.3172 m^3/kg

next we calculate the mass flow rate of Oxygen

m =
`(A1V)/(v1)` ----- ( 2 )

A1 ( area of pipe ) = 0.0113 m^2 ( calculated )

V = 70 m/s

V1 = 0.3172 m^3/kg

substitute value into equation 2

m ( mass flow rate of oxygen ) = 2.4936 kg/s

Finally calculate the rate at which entropy is generated in the pipe

S =
`m( C_(p) In(T2)/(T1) - RIn(P2)/(P1) )` --------- ( 3 )

`C_(p)` = 0.918 kj/kgk ( property of oxygen )

T2 = 291 k

T1 = 293 k

P2 = 200 kPa

P1 = 240 kPa

substitute values into equation 3 above

S = 0.10253 kW/k