Should the air specific heat ratio be included in the ideal gas law ? 1

[Ameen1985]

As you can see, both equations use the ideal gas low with the universal gas constant in J/kg.k
Both equations are used in published articles as follows:
"Application of dynamic programming to the optimal management of a hybrid power plant with wind turbines, photovoltaic panels and compressed air energy storage" and "Design and thermodynamic analysis of a multi-level underwater compressed air energy storage system"
Should the air specific heat ratio "K" be included in the ideal gas law or not ?

 

[pierreick]

Hi,
Isothermal means PV=cte =RT.
my 2 cents
Pierre

 

[Snickster]

No the ratio of specific heats "k" is not part of the ideal gas equation of state.

The second equation you shows the ideal gas equation applied to the addition of mass to a constant pressure cavern/reservoir, such as CAES storage underwater, in constant pressure varriable volume storage units. In this case the relation between pressure and mass can be detrmined using the ideal gas equation considering a constant pressure and temperature process:

PV = mRT
d(PV) = d(mRT)

Since P, R and T are constant they can be taken out of the differential so that:

P(dV) = RT(dm) or

dm = (P/RT) dV

The first equation is not the ideal gas equation. The first equation calculates dP/dt for a constant volume cavern/reservoir (such as a salt dome) that increases in pressure as mass is added at constant volume of the cavern/reservoir. This equation is derived by balance of energy considerations with the control volume being the cavern/resevoir. The attached paper Part 3.1 shows the derivation. Unfortunately it does not show all steps of the derivation but in any case it is based on the first law of thermodymanics energy balance.