Consider an insulated system containing 150 g of liquid water and 150 g of ice at equilibrium under atmospheric pressure. A total of 22g of steam at 120◦C is admitted to the system. What is the phase composition and temperature when equilibrium is reestablished?
To find the phase composition and temperature when equilibrium is reestablished in the system, we need to consider the energy balance.
First, let's find the energy involved in each phase transition:
1. Heating the ice from 0°C to its melting point: ΔQ1 = m * c_ice * ΔT
- Here, m is the mass of ice (150 g), c_ice is the specific heat capacity of ice, and ΔT is the temperature change (0°C to the melting point of ice).
2. Melting the ice at its melting point: ΔQ2 = m * ΔH_fusion
- ΔH_fusion is the heat of fusion of ice.
3. Heating the liquid water from the melting point to the final temperature: ΔQ3 = m * c_water * ΔT
- Here, c_water is the specific heat capacity of water, and ΔT is the temperature change from the melting point to the final temperature.
4. Vaporizing the water at the final temperature: ΔQ4 = m * ΔH_vaporization
- ΔH_vaporization is the heat of vaporization of water.
The total energy change is given by the sum of all these individual energy changes: ΔQ_total = ΔQ1 + ΔQ2 + ΔQ3 + ΔQ4
Now let's calculate the energy changes involved:
1. Heating the ice to its melting point:
- The specific heat capacity of ice (c_ice) is approximately 2.093 J/g°C.
- The temperature change (ΔT) is (0°C - (-10°C)) = 10°C.
- Therefore, ΔQ1 = m * c_ice * ΔT = 150 g * 2.093 J/g°C * 10°C = 3139.5 J
2. Melting the ice at its melting point:
- The heat of fusion of ice (ΔH_fusion) is approximately 334 J/g.
- Therefore, ΔQ2 = m * ΔH_fusion = 150 g * 334 J/g = 50100 J
3. Heating the liquid water from the melting point to the final temperature:
- The specific heat capacity of water (c_water) is approximately 4.18 J/g°C.
- The temperature change (ΔT) is (final temperature - 0°C).
Since the system is at equilibrium and under atmospheric pressure, the final temperature will be the boiling point of water (100°C).
- Therefore, ΔT = 100°C - 0°C = 100°C
- Therefore, ΔQ3 = m * c_water * ΔT = 150 g * 4.18 J/g°C * 100°C = 62700 J
4. Vaporizing the water at the final temperature:
- The heat of vaporization of water (ΔH_vaporization) is approximately 2260 J/g.
- Therefore, ΔQ4 = m * ΔH_vaporization = 150 g * 2260 J/g = 339000 J
Now, let's calculate the total energy change:
ΔQ_total = ΔQ1 + ΔQ2 + ΔQ3 + ΔQ4
= 3139.5 J + 50100 J + 62700 J + 339000 J
= 455939.5 J
Since the system is insulated, the total energy change must be zero for equilibrium. Therefore:
ΔQ_total = 0
455939.5 J = 0
Since this equation is not satisfied, it means that equilibrium cannot be reestablished. The system will not reach a phase composition and temperature where both ice and water remain stable in equilibrium.