Question

Steam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 3.2 kg/s and leaves at 20 kPa. If the power output of the turbine is 2.5 MW, determine the temperature of the steam at the turbine exit. Neglect kinetic energy changes. Use data from the steam tables.

Answer 1

Answer:

The temperature of the steam at turbine exit is $T_{2}$ = 1190.26 K

Explanation:

Given data

$T_{1} = 500$°c = 773 K

Mass flow rate = 3.2 $\frac{kg}{s}$

Power output = 2.5 MW = 2500 KW

From steady flow energy equation

$h_{1} + KE_{1} + PE_{1} + Q = h_{2} + KE_{2} + PE_{2} + W$

Since Kinetic & potential energy changes are negligible.

$h_{1} + Q = h_{2} + W$

Since turbine  is adiabatic so Q = 0

$h_{1} = h_{2} + W$

$h_{1} - h_{2} = W$

$m C_{p} (T_{2} - T_{1} ) = W$

Put all the values in above equation

3.2 × 1.8723 × ( $T_{2}$ - 773 ) = 2500

$T_{2}$ - 773 = 417.26 K

$T_{2}$ = 1190.26 K

This is the temperature of the steam at turbine exit.