i have studied everywhere that both coefficient of compressiblity and isothermal compressiblity are reciprocal to bulk modulus of material. then what is the difference between that two?
I think you are right - Young's modulus is calculated at room temperatures so far as compressibility is concerned but for isothermal compressibility I think you can consider a isothermal field through the homogenous material and consider a spring positioned in it (probably a D-Branes String (Mallick (2014)) on my RG page of the same material and consider its elasticity properties at the given temperature and density which will really be like the oscillating velocity of a wave. SKM
Isothermal compressibility is a term often used in thermodynamics in relation to gases. Mathematically, expressed as k = -(dP/dV) at constant T (absolute). Now the derivatives should be read as partial derivatives. The negative sign is for inverse relation between pressure and volume. The ratio can be calculated from gas laws (ideal or real). Hope that somewhat clarifies your doubts.
Dear Mangalya, I am sorry your definition is false.
Isothermal compressibility defined by KappaT = - 1/V (dV/dP)T or = - (dLnV/dP)T , You may also define the adiabatic compressibility as Kappaad = - (dLnV/dP)S under the constant entropy. We have following thermodynamic connections as well in terms of enthapy H and Gibbs free energy G:
V= (dH/dP)S V=(dG/dP)T where d denotes partial differential operator.
If some body talks about careless just calling as 'compressibility' he/she means isothermal compressibility. For solids the difference between the adiabatic and isothermal compressibilities is almost negligible, since the ratio of kappa adiabatic versus Kappa isothermal = Specific Heat ratio under the constant volume versus constant pressure, which is almost unity for solids.
Kappaad /KappaT = CV / CP about unity for solids
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