Drawing constant property lines on p-v/T-s/u-s diagrams

[Urmi Roy]

Hi All,

I'm really curious to know how we can predict the shapes of constant property lines (isenthalpic/constant internal energy/isotherms/isentropes/isobars) on any given plot, such as T-s and P-v or even u-s diagrams. Is there a rule to do so? Usually in practice we deal with p-v and T-s diagrams, but other types of plots also exist.

 

[Simon Bridge]

You use the equation of state.
Take the PV diagram: can you see why a constant volume line will be vertical ad the constant pressure line will be horizontal?

The equation of state is (probably) the ideal gas law: PV=nRT ... if temperature is a constant for an isotherm, then P=<constant>/V ... so the isotherm has to have a 1/V shape.

Now extrapolate for the others you are interested in.

 

[Urmi Roy]

You use the equation of state.
Take the PV diagram: can you see why a constant volume line will be vertical ad the constant pressure line will be horizontal?

The equation of state is (probably) the ideal gas law: PV=nRT ... if temperature is a constant for an isotherm, then P=<constant>/V ... so the isotherm has to have a 1/V shape.

Now extrapolate for the others you are interested in.

I'm referring to pure substance P-v/T-s diagrams. Therefore in the vapor dome, no particular constitutive relation exists.

I don't see how can simply extrapolate (again considering the pure substance model) to get things such as constant enthalpy/entropy/internal energy etc lines.

 

[Chestermiller]

I'm referring to pure substance P-v/T-s diagrams. Therefore in the vapor dome, no particular constitutive relation exists.

I don't see how can simply extrapolate (again considering the pure substance model) to get things such as constant enthalpy/entropy/internal energy etc lines.

At pressures that are low compared to the critical pressure (so that the gas phase behavior approximates an ideal gas), this portion of the diagrams can be approximated very accurately from scratch. All you need to know are the heat capacities of the liquid and the gas as a function of temperature, the heat of vaporization at one temperature, the equilibrium vapor pressure at one temperature, and the specific volume of the liquid as a function of temperature. At higher pressures, filling in these diagrams is more complicated, and requires equation of state data.

Chet

 

[PJC01]

I am familiar with the concept of constant property lines on p-v/T-s/u-s diagrams. These lines represent the relationship between different thermodynamic properties at constant values. In order to predict the shape of these lines on a given plot, we must first understand the fundamental principles of thermodynamics and the properties that are being represented.

For example, on a p-v diagram, the isotherms (lines of constant temperature) will have a positive slope due to the ideal gas law (PV = nRT). As the temperature increases, the volume must also increase in order to maintain a constant pressure. On the other hand, the isobars (lines of constant pressure) will have a negative slope as the volume decreases with increasing pressure.

Similarly, on a T-s diagram, the isentropes (lines of constant entropy) will have a positive slope due to the relationship between temperature and entropy (dS = dQ/T). As the temperature increases, the amount of heat required to maintain a constant entropy also increases. The isenthalpic and constant internal energy lines will have different shapes depending on the specific properties being held constant.

In order to accurately predict the shape of these lines, it is important to have a thorough understanding of the thermodynamic properties being represented and their relationships. Additionally, the type of substance being analyzed (ideal gas, real gas, liquid, etc.) will also affect the shape of these lines.

In practice, these constant property lines are used to analyze and understand the behavior of substances under different thermodynamic conditions. By studying the shape and location of these lines on a diagram, we can make predictions and calculations about the behavior of the substance.

In conclusion, there is no one rule to predict the shape of constant property lines on p-v/T-s/u-s diagrams. It requires a thorough understanding of thermodynamics and the properties being represented, as well as the substance being analyzed. These diagrams are valuable tools for scientists to study and analyze the behavior of substances under different thermodynamic conditions.