Question

Air at 510°C and 450 kPa enters an ideal, polytropic and adiabatic turbine. The exit pressure is 101 kPa. In steady state, the turbine produces 50 kW of power. Find the:

a. Exit temperature
b. Mass flow rate

Answer 1

Answer:511 K

Step-by-step explanation:

Given

`T_1=510^(\circ) C\approx 783\ K`

`P_1=450\ KPa`

`P_2=101\ KPa`

Power Produces
`W=50\ kJ`

For Polytropic Process

`(T_2)/(T_1)=[(P_2)/(P_1)]^{(k-1)/(k)}`

For air
`k=1.4`

`(T_2)/(T_1)=[(P_2)/(P_1)]^{(k-1)/(k)}`

`(T_2)/(783)=[(101)/(450)]^{(1.4-1)/(1.4)}`

`(T_2)/(783)=[(101)/(450)]^(0.2857)`

`T_2=783* 0.652`

`T_2=510.94\ K\approx 511\ K`

(b)

`W=\dot{m}c_p(T_1-T_2)`

`50=\dot{m}* 1.005* (783-511)`

`\dot{m}=(50)/(273.36)`

`\dot{m}=0.183\ kg/s`