# Are theses approaches correct? (entropy change of water turning into steam)

• EastWindBreaks
In summary, an electric resistance heater transfers 2200 kJ of energy to saturated water and determines the entropy change of the water.
EastWindBreaks

## Homework Statement

An insulated piston-cylinder device contains 5 L of saturated liquid water at a constant pressure of 150 kPa. An electric resistance heater inside the cylinder is now turned on, and 2200 kJ of energy is transferred to the steam. Determine the entropy change of the water during this process

## Homework Equations

Steam tables
h_f1= specific enthalpy of saturated water in state 1
h2= specific enthalpy in state 2?
h_g2= specific enthalpy of saturated vapor in state 2
h_f2=specific enthalpy of saturated liquid in state 2 =h_f1

## The Attempt at a Solution

My first approach:
Step 1: since it has moving boundary work, Q_in=ΔU+W=ΔH=m(h2-h_f1), using steam tables to find the specific volume and specific enthalpy of saturated water at 150 kPa use them to find h2

Step 2: with P=150 kPa, and h2 is known, I need to know which phase is the water in, so I go to saturated water table and I see h_f< h2 <h_g, so it is saturated-liquid mixture, I get to use specific enthalpy of saturated water and vapor from saturated water table. find quality X from h2= h_f2+X(h_g2- h_f2)
( correct me if I am wrong please)

Step 3: with quality X known, I can find s2 from s2= s_f+X(s_fg), and those properties are from saturated water table as well. then finally ΔS= m(s2-s1)=5.72 KJ/K

when I try to check my solution, I saw this approach from chegg:

this approach looks more straightforward, but I am confused on how its using latent heat of vaporization to check if water change phase or not, since latent heat of vaporization requires constant temperature process but the temperature information is not given, and it concludes the temperature is constant from no phase change, though, temperature can change without phase change right?

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Last edited:
Ignore MechRock: it's totally wrong (where he says 'there will not be any phase change').
Your scenario looks a lot better than his. Get started: what is h_f1 ? You'll also need s_f1.

Last edited:
EastWindBreaks
EastWindBreaks said:
constant temperature process but the temperature information is not given
Indirectly it is: 'saturated at 150 kPa' -- Mech looked it up for you.

EastWindBreaks
BvU said:
Ignore MechRock: it's totally wrong (where he says 'there will not be any phase change').
Your scenario looks a lot better than his. Get started: what is h_f1 ? You'll also need s_f1.
Thank you!

Your step 1 is correct. Once you see that ##h_2-h_{f1}## is less than the heat of vaporization, you know that not all the water has evaporated. So you know that the process takes place at constant pressure and temperature, and $$\Delta S=Q/T$$However, there is nothing wrong with the way that you solved it.

EastWindBreaks
Chestermiller said:
Your step 1 is correct. Once you see that ##h_2-h_{f1}## is less than the heat of vaporization, you know that not all the water has evaporated. So you know that the process takes place at constant pressure and temperature, and $$\Delta S=Q/T$$However, there is nothing wrong with the way that you solved it.
Thank you, but how do you know its a constant temperature process from the fact that it's in liquid-vapor mixture state?

EastWindBreaks said:
Thank you, but how do you know its a constant temperature process from the fact that it's in liquid-vapor mixture state?
They told you that the pressure is held constant, so, for vaporization of a pure liquid at constant pressure, the temperature is constant.

EastWindBreaks
Chestermiller said:
They told you that the pressure is held constant, so, for vaporization of a pure liquid at constant pressure, the temperature is constant.
is there an equation that shows this relationship?

EastWindBreaks said:
is there an equation that shows this relationship?
Didn't they teach you that as a pure liquid vaporizes at constant pressure, its temperature stays constant. We know that when you boil water at 1 atm pressure, for example, its temperature remains constant at 100 C until it is all gone. The Clausius-Clapeyron equation describes the relationship between the equilibrium vapor pressure and the equilibrium temperature of a pure substance.

EastWindBreaks
Chestermiller said:
Didn't they teach you that as a pure liquid vaporizes at constant pressure, its temperature stays constant. We know that when you boil water at 1 atm pressure, for example, its temperature remains constant at 100 C until it is all gone. The Clausius-Clapeyron equation describes the relationship between the equilibrium vapor pressure and the equilibrium temperature of a pure substance.
oh wow , yeah, I can't believe I forgot about that..I was reading that part just two weeks ago, thank you!

## 1. What is entropy change?

Entropy change is a measure of the disorder or randomness of a system. In the context of water turning into steam, it refers to the change in the distribution and arrangement of water molecules as they transition from a liquid state to a gaseous state.

## 2. Why is the entropy change of water turning into steam important?

The entropy change of water turning into steam is important because it is a fundamental thermodynamic property that helps us understand the behavior of matter and energy. It is also crucial in many industrial processes, such as power generation and refrigeration.

## 3. How is the entropy change of water turning into steam calculated?

The entropy change of water turning into steam can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat absorbed or released during the phase change, and T is the temperature at which the phase change occurs.

## 4. Are there any limitations to these approaches in calculating entropy change?

Yes, there are limitations to these approaches in calculating entropy change. These calculations assume ideal conditions and do not take into account factors such as pressure and non-ideal behavior of water molecules. Additionally, these equations may not accurately reflect the true entropy change in complex systems.

## 5. How does the entropy change of water turning into steam relate to the laws of thermodynamics?

The entropy change of water turning into steam relates to the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. As water turns into steam, the randomness and disorder of the system increases, leading to a positive change in entropy.

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