Institute of Sciences (CUT) L2GP
Department of Process Engineering 2024/2025
SERIES N°03:
CHANGES OF A PURE BODY AND PHASE EQUILIBRIUM
Exercise N°01
In a 150 liter flask, 1.4 kg of water has been introduced of water at a pressure of 1 bar. The
flask was then heated until the internal pressure reached 16.5 bars. What is the composition
of the fluid contained in the flask?
Data:
From the table of thermodynamic properties of saturated steam, v' = 0.12 m3/kg.
Exercise N°02
Consider a system initially composed of a mass m of a pure solid at a temperature T0 below
the melting temperature. This system receives a certain amount of heat from the external
environment, and in its final state, the substance is in vapor form. The diagram below
shows the change of phases of a substance on a temperature vs time
graph on heating the substance at a constant rate.
Calculate:
1) The amount of heat Q1 received by the system during heating to Tmelt.
2) The heat Q2 absorbed by the system during the change of state: solid-liquid.
3) The quantity of heat Q3 received by the system causing the mass m of the liquid to
heat up to its boiling temperature.
4) The quantity of heat Q4 received by the system, causing total vaporization of the mass
m of liquid (change of state: liquid-vapor).
For water at atmospheric pressure:
The mass of the system is m = 1g of ice; T0= -20°C; P =1 bar; Tmelt = 0°C and
Tvap.= 100°C; Lf (0°C)=335 kJ/kg; Lv (100°C) = 2250 kJ/kg.
Specific heats are considered constant over the temperature range (-20°C to 100°C):
Dr . BELALIA FATIHA 1
Institute of Sciences (CUT) L2GP
Department of Process Engineering 2024/2025
Cps = 2.1 kJ/kg.K; CpL = 4.18 kJ/kg.K.
Exercise N°03
A 1200 W immersion heater is placed in a beaker containing water. From the moment the
water begins to boil, calculate the time required for 500 g of water to vaporize. Heat losses are
neglected. Lv = 23.105 J/kg.
Exercise N°04
a) The melting point of aluminum is 660°C, its latent heat of fusion is 397kJ/kg, and its
specific heat is 900J/kg.K. How much heat must be added to 150 kg of aluminum
originally at 25°C to completely melt it? This amount of heat is produced by an electric
furnace with an overall efficiency of 60%.
b) Calculate the electrical energy used.
Exercise N°05
The following figure shows a set of experimental curves, called Andrews isotherms,
representing the pressure P of one mole of a fluid as a function of the volume Voccupied, for
different temperatures, (Clapeyron diagram).
1. Determine the coordinates (PC, VC) of critical point C.
2. Specify the physical state of the fluid and calculate the molar titles xv and xL of steam
and liquid for :
V = 0.6 liters and T = 10°C.
P = 110 bar and T = 200 °C
V = 0.2 liters and T = 125 °C
3. What is the molar volume of dry saturated steam at a pressure of 40 bars?
Dr . BELALIA FATIHA 2
Institute of Sciences (CUT) L2GP
Department of Process Engineering 2024/2025
Exercise N°06 (Phase balance)
1. What is the normal boiling temperature of pure liquids A and B?
2. Which is the more volatile liquid?
3. Are the two liquids A and B miscible in all proportions?
4. At what temperature does a mixture of mole fraction xA = 0.1 begin to boil, at 1 atm?
5. Index the diagram (on the diagram).
6. At 95°C and 1 atm, what are the compositions of the liquid and vapor in equilibrium?
7. At what temperature does boiling of a liquid with mole fraction XA = 0.40 at 1 atm
end?
8. At what temperature does a vapor with mole fraction xAV = 0.5 begin to condense at 1
atm?
9. Colour the dew point curve blue.
10. At what temperature does condensation of a molar vapor xAV = 0.4 at 1 atm end?
11. What is the composition of the first drop of liquid (in equilibrium with the vapor)
formed during condensation of a vapor with mole fraction XB = 0.5 at 1 atm?
12. What is the composition of the last drop of liquid (in equilibrium with the vapor)
remaining when vaporizing a mixture of composition xA = 0.20 at 1 atm?
13. A mixture of composition 0.50 is heated to 70°C. What are the compositions and
nature of the different phases in equilibrium?
14. A mixture with molar fraction xA = 0.3 is heated to 80°C, under 1 atm. Knowing that
this mixture contains 100 moles, how many moles of A are transformed into steam at
80°C?
Dr . BELALIA FATIHA 3
