# Thermodynamics - Help me understand phase diagrams

• Hercuflea
In summary, the thermo professor has been emphasizing phase diagrams in lieu of analytical problems, but the labels on the axes have not been provided. The student is having difficulty locating the water's state on the T-V diagram because the graph is scaled logarithmically. The student is then supposed to interpolate by eyeball to find the water's temperature. If the student is uncomfortable with logarithmic coordinates, he or she can try to find the data point on the graph and qualitatively determine where it is in the superheated and saturated regions.
Hercuflea

## Homework Statement

So my thermo professor has been putting a huge emphasis on phase diagrams, which I didn't really expect. He basically skips most of the analytical/calculus type problems and gives us the graphical phase diagram/ "real world" type of problems for homework. I don't understand phase diagrams because they never put any labels on the axes, and it is just like a little parabola and then he draws two horizontal lines through it, but nothing is labeled.

So here's the problem :

For H2O, determine the specific property at the indicated state. Locate the state on a sketch of the T-V diagram.

a) p = 300 kPa, v (specific volume) = .5 m^3/kg Find T, in Celsius.

## Homework Equations

PV^n = k, k is a constant

## The Attempt at a Solution

I have a table where I can look up these things but it says that water at 300 kPa (3 bar) is supposed to be .6058 m^3/kg not .5 m^3/kh. So I guess the water in this problem is not saturated and I can't use my table? How can I tell?

And once I find the temperature how do I draw the diagram?

Google T-V diagram. One of the figures it will show you will be a t-v diagram for water. Click on it. Find your point on the diagram.

Ok I have done this. But the graph is scaled logarithmically or something and my answer would not be exact. Am I just supposed to just guess what the temperature is between 100C and 200C?

Hercuflea said:
Ok I have done this. But the graph is scaled logarithmically or something and my answer would not be exact. Am I just supposed to just guess what the temperature is between 100C and 200C?

Yes. That's how you would use any graph. You have to interpolate as best you can by eyeball. Are you uncomfortable with logarithmic coordinates? If so, get used to it. Find a piece of logarithmic graph paper with a more detailed grid on it to see how the numbers space out, or get yourself a slide rule (which has logarithmic scales on it). Try to find the location of your data point as closely as possible on the graph and see if you can at least see what region it is in qualitatively. For example, is it in the superheated region or in the saturated region?

chet

I can understand your confusion with phase diagrams. They can be quite complex and difficult to interpret without proper labeling and understanding of the axes. Phase diagrams show the relationship between pressure, temperature, and the physical state of a substance. The horizontal lines you mentioned represent the coexistence of two phases, while the parabola represents the boundary between liquid and gas phases.

In order to solve the problem, you will need to use the ideal gas law, which is PV = nRT. This equation relates pressure, volume, temperature, and the number of moles of a gas. In this case, you are given the pressure and specific volume of water, and you are asked to find the temperature. You can rearrange the ideal gas law to solve for temperature, which will give you the temperature in Kelvin. To convert to Celsius, simply subtract 273.15 from the temperature in Kelvin.

As for drawing the diagram, you can use the given pressure and specific volume to locate the point on the T-V diagram. On the x-axis, you will have specific volume and on the y-axis, you will have temperature. Once you have located the point, you can draw a vertical line from that point to the parabola, which will give you the corresponding temperature. I suggest reviewing the concepts of phase diagrams and ideal gas law to fully understand the problem and how to solve it. I hope this helps!

## 1. What is a phase diagram?

A phase diagram is a graphical representation of the different phases (solid, liquid, and gas) that a substance can exist in under different combinations of temperature and pressure.

## 2. How do you read a phase diagram?

To read a phase diagram, you need to locate the point on the graph that corresponds to the temperature and pressure of the substance. This point will determine which phase the substance is in at that particular temperature and pressure.

## 3. What is the significance of the triple point on a phase diagram?

The triple point is the point on a phase diagram where all three phases (solid, liquid, and gas) coexist in equilibrium. It represents the unique combination of temperature and pressure at which the substance can exist in all three phases simultaneously.

## 4. How is a phase diagram useful in understanding thermodynamics?

A phase diagram helps us understand the relationship between temperature, pressure, and the different phases of a substance. It also provides information about the conditions under which a substance can undergo phase transitions, and the energy changes that occur during these transitions.

## 5. What factors can affect the shape of a phase diagram?

The shape of a phase diagram can be affected by factors such as the chemical composition of the substance, the strength of intermolecular forces, and the presence of impurities. Changes in these factors can cause shifts in the phase boundaries and alter the shape of the phase diagram.

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