Question

Consider now a turbine that operates with steam with T1 = 450◦C and P1= 8.0 MPa and P2 = 30 kPa. The efficiency is 80% and the mass flow rate is 80 kg/s. You may assume the velocities are zero. You may also assume q=0.

a. What is the exhaust temperature and for 100% efficiency?

b. What is the output temperature for 80% efficiency?

Answer 1

a)

For this we will make use of steam table and obtain the value of specific enthalpy required to solve the problem

For state 1

P = 8 MPa

T =450 oC

at this pressure and temperature

H = 3273.234 KJ/Kg

s = 6.5576 KJ/KgK

Now here q is zero and hence the process is adiabatic

Now if the efficiecy is 100 % it implies that the process can be assumed to be reversible

A reversible adiabatic process is nothing but isentropic process

hence the entropy will not change

Hence we will look at State in steam table Having P = 30 KPa and S = 6.5576 KJ/KgK

From steam table

at P = 30 Kpa saturated liquid has entropy has Sv = 7.7674 KJ/Kg K and Sl = 0.94393 KJ/Kg K

Hence the outlet stream is actually saturated

The temeperature will be the saturation temperature at P =30 KPa

Tsat = 69.09 oC

We can find the quality of steam as following

S =x*Sv + (1-x)*Sl

6.5576 = x*7.7674 + (1-x)* 0.94393

x = 0.823

Hence the exhaust temperature of steam in 69.09 oC

quality of steam is 0.823 for 100 % efficiency

H = x*Hs + (1-x)*Hl = 0.823*2624.551+ (1-0.823)*289.22= 2211.1997 KJ/Kg

b) For this we will find work requried 100 % efficiency and than take 80 % of that which will be the actual work

Hence

Wideal = (Hin -Hout) = 3273.234- 2211.1997 = 1062.0343 KJ/Kg

Wactual = 0.8*1062.0343 = 849.627 KJ/Kg

Wactual = Hin - Hout

849.627 = 3273.234 -Hout

Hout = 2423.607 KJ/Kg

now we will look in the steam table and find the value if T corresponding to the value of P =30 KPa and H = 2423.607 KJ/Kg

The steam will still be Saturated in this case So the temperature will remain the same , the vapor fraction however will vary this time

H =x*Hv + (1-x)*Hl

2423.607 =  x*2624.551+ (1-x)*289.22

x = 0.91397