Water at 70 kPa and 100degreeC is compressed isentropically

Water at 70 kPa and 100degreeC is compressed isentropi-cally in a closed system to 4 MPa. Determine the final temperature of the water and the work required, in kJ/kg, for this compression.

Solution

Given

P1 = 70 kPa

T1 = 100 C

Note the properties of water at P1 and T1

u1 = 2510 kJ/kg

s1 = 7.534 kJ/kg-K

Since the process is isentropic

s2 = s1 = 7.534 kJ/kg-K

Also P2 = 4 Mpa

Note the properties of water at s2 and P2

T2 = 664.8 C

u2 = 3397 kJ/kg

From the first lae

Q = du +W

Here Q = 0 (since it is isentropic process)

W = -du = u1-u2 = 2510-3397

W = -887 kJ/kg

Therefore the work required is 887 kJ/kg