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