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Mechanical Properties Of Fluids

Question
CBSEENPH11019691

Define bulk modulus. Find the bulk modulus of gas for isothermal, adiabatic, isobaric and isochoric processes.

Solution
The bulk modulus of gas is defined as the ratio of the change in pressure of the gas to the volume strain in it.
It is given by, 
straight K space equals space minus space straight V space dP over dV

For space isothermal space process comma

space PV space equals space constant.

So comma space dP over dV equals space minus straight P over straight V

therefore space straight K space equals space minus space straight V space dP over dV space equals space straight P space

For space adiabatic space process comma space

PV to the power of straight gamma space equals space constant

So comma space

space space space space space space dP over dV space equals space minus straight gamma space straight P over straight V

therefore space straight K space equals space minus straight V space dP over dV space equals space γP space

For space isobaric space process comma space

straight P space equals space constant

That space is comma space

dP over dV space equals space 0

therefore space straight K space equals space minus straight V space dP over dV space equals space 0 space
For space isochoric space process comma space

straight V space equals space constant

rightwards double arrow space dP over dV space equals space infinity space

therefore space straight K space equals space minus straight V space dP over dV space equals space infinity space