Solved Problems on Steam Properties

SOLVED PROBLEMS ON STEAM PROPERTIES

Problem 4.1

Determine the state of steam at a pressure of 12 bar with its specific volume of 0.175 m3/kg.

Given data:

p = 12 bar

v = 0.175 m3/kg

To find:

State of steam (whether dry, wet or superheated)

Solution:

From saturated water table of pressure scale at 12 bar,

Specific volume of dry steam, vg = 0.16321 m3/kg, T, =188°C = 188 + 273 = 461 K 

Since v > vg, the steam is in superheated condition.

Note:

v > vg ⇒ Superheated steam

v = vg ⇒ Dry steam

v < vg ⇒ Wet steam

Problem 4.2

Determine the condition of steam at a temperature of 220°C and enthalpy of 2750 kJ/kg.

Given data:

T = 220°C

h = 2750 kJ/kg

To find:

State of steam

Solution:

From saturated water table of temperature scale at 220°C,

hf = 943.7 kJ/kg

hfg = 1856.2 kJ/kg

hg = 2799.9 kJ/kg

Since h < hg, the steam is in wet condition.

Note:

h > hg ⇒ Superheated steam

h = hg ⇒ Dry steam

h < hg ⇒ Wet steam

Problem 4.3

Find the specific volume and enthalpy of steam at 9 bar when the condition of steam is (a) wet with dryness fraction 0.98 (b) dry saturated and (c) superheated and the temperature of steam 240°C.

Given data:

p = 9 bar

(i) x = 0.95, (ii) x = 1, (iii) Superheated with Tsup = 240°C = 240 + 273 = 513 K

Solution:

From saturated water table of pressure scale at 9 bar,

Ts = 175.4°C = 175.4 + 273 = 448.4 K

vf = 0.001121 m3/kg 

vg = 0.21482 m3/kg

hf = 742.6 kJ/kg

hfg = 2029.5 kJ/kg

hg = 2772.1 kJ/kg

Problem 4.4

Find the internal energy of unit mass of steam at a pressure of 7 bar (i) when its quality is 0.8 (ii) when it is dry and saturated and (iii) superheated, the degree of superheat being 65°C. The specific heat of superheated steam at constant pressure is 2.277 kJ/kg K. 

Given data

p = 7 bar = 700 kPa

(i) x = 0.80

(ii) dry saturated and

(iii) Superheated, (Tsup - Ts) = 65°C

To find

Internal energy

Solution

From saturated water table of pressure scale at 7 bar,

T1 = 165°C,

vf = 0.001108 m3/kg,

vg = 0.27268 m3/kg

hfg = 2064.9 kJ/kg

hf = 697.1 kJ/kg,

hg = 2762 kJ/kg,

Sf = 1.992 kJ/kg K

Sfg = 4.713 kJ/kg K

Sg = 6.705 kJ/kg K

Problem 4.5

Determine the condition of steam whether it is wet, dry or superheated for the following cases by using Steam tables only.

(i) Steam has a pressure of 10 bar and specific volume 0.22 m3/kg. 

(ii) Steam has a pressure 15 bar and temperature 225°C.

(iii) Steam has a temperature 200°C and enthalpy 2790.9 kJ/kg. 

(iv) Steam has a temperature of 120°C and entropy 7 kJ/kgK. 

Given data:

(i) p = 10 bar and v = 0.22 m3/kg

(ii) p = 15 bar and T = 225°C

(iii) T = 200°C and h = 2790.9 kJ/kg

(iv) T = 120°C and s = 7 kJ/kg K

To find:

Condition of steam

Solution:

(i) p = 10 bar and v = 0.22 m3/kg

From saturated water table of pressure scale at 10 bar, vg = 0.1943 m3/kg

Since v > vg, the steam is superheated. Ans.

(ii) p = 15 bar and T = 225°C

From saturated water table of pressure scale at 15 bar, Ts = 198.3°C

Since T > Ts, the steam is superheated. Ans.

(iii) T = 200°C and h = 2790.9 kJ/kg

From saturated water table of temperature scale at 200°C, hg = 2790.9 kJ/kg

Since h = hg, the steam is dry saturated. Ans.

(iv) T = 120°C and s = 7 kJ/kgK

From saturated water table of temperature scale at 120°C, sg = 7.129 kJ/kg K 

Since s < sg, the steam is in wet condition. Ans.

Problem 4.6

One kg of steam contains 1/3 liquid and 2/3 vapour by volume. The temperature of the steam is 150°C. Find the quality, specific volume and specific enthalpy of mixture.

Given data:

m = 1 kg

Vf = 1/3

Vg = 2/3

T3 = 150°C

To find:

Quality x, specific volume, v and specific enthalpy, h

Solution:

From saturated water table of temperature scale at 150°C,