How Does Adiabatic Compressibility of an Ideal Gas Compare to Isothermal?

[Milly_S]

I have been asked to show that if an ideal gas is compressed isothermally its compressibility is 1/P whereas if the same gas is compressed adiabatically its compressibility is 1/yP

Where y is gamma


I have managed to do the first bit about isothermal compressibility, but cannot work out how to do the next bit.

 

[Andrew Mason]

I have been asked to show that if an ideal gas is compressed isothermally its compressibility is 1/P whereas if the same gas is compressed adiabatically its compressibility is 1/yP

Where y is gamma


I have managed to do the first bit about isothermal compressibility, but cannot work out how to do the next bit.

Define compressibility first. Then show us your work for the isothermal case.

Write out the expression for compressibility in the adiabatic case (how are P and V related in a (reversible) adiabatic compression?).

AM