A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is
Modulus refers to a measure of a material’s stiffness or resistance to deformation under stress. It quantifies the relationship between stress and strain in elastic materials. Common types include Young’s modulus for tensile stress shear modulus for shear stress and bulk modulus for volumetric stress each indicating how materials respond to different forces.
Class 11 Physics Chapter 8 explores the mechanical properties of solids focusing on concepts such as stress strain and elasticity. It examines how solids deform under various forces and their ability to return to original shapes. Important topics include Hooke’s law different types of stress and strain and practical applications in engineering and material science.
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To find the isothermal bulk modulus K of an ideal gas we can use the formula:
K = – V (∂P/∂V)_T
For an ideal gas at constant temperature (isothermal) the relation between pressure P and volume V is given by Boyle’s Law:
PV = nRT
Differentiating this equation while keeping the temperature constant gives us:
∂P/∂V = -nRT/V²
Thus the isothermal bulk modulus becomes:
K = -V (-nRT/V²) = nRT/V
Since nRT = PV we can substitute that in the equation too;
K = PV/V = P
Thus the isothermal bulk modulus of the gas is:
K = P
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