Which Gas Is More Compressible: Isothermal or Isentropic?

[Perodamh]

Homework Statement

Gas A at 125KPa (abs) is compressed isothermally and gas B at 100kPa(abs) is compressed isentropically (Y = 1.4). Which gas is more compressible?[/B]

Homework Equations

Compressibilty = 1/bulk's modulus
Bulk's modulus = F/A/V/v or volume stress/volume strain

The Attempt at a Solution

I'm not sure I'm using the right equation , I've also tried Q= w(Y-n)/(y-1), but for an adiabatic compression Q is always 0, so does that mean the isothermally compressed gas is more compressible??[/B]

 

[lippyka]

The answer is that the isothermally compressed gas is more compressible. The bulk modulus of a gas is defined as the pressure increase needed to cause a unit decrease in volume. Since the isothermal compression process involves no change in temperature, the increase in pressure causes a relatively large decrease in volume, making the gas more compressible. The isentropic compression process involves a change in temperature, which tends to reduce the amount of volume change for a given increase in pressure, making the gas less compressible.