- #1
PKM
- 49
- 16
Homework Statement
:[/B]
A gas obeying the equation of state [itex]PV=RT[/itex] undergoes a hypothetical reversible process [tex]
PV^\frac{5}{3} e^\frac{-PV}{E_0} = c_1[/tex] Can we prove that the thermal compressibility of the gas undergoing this process tends to a [itex]constant[/itex] value at very high temperature? Here, [itex]E_0[/itex] and [itex]c_1[/itex] are constants with dimensions.
Homework Equations
The thermal compressibility of a gas is given as [tex]\kappa = \frac{-1}{V} \frac{\delta V}{\delta P}[/tex]
The Attempt at a Solution
First I tried to find the thermal compressibility using the above differential equation, considering the reversible process given. I made use of the equation of state [itex]PV = RT[/itex], to substitute [itex]RT[/itex] for [itex]PV[/itex]. My result contains a term P, which cannot be cancelled, or substituted to yield a constant value, at very high temperatures.
Any solution, or comment?