Properties of Bulk Matter

The One Thing

Properties of bulk matter describe how solids deform and recover, and how fluids exert pressure, form surfaces, and flow. These behaviours are explained through restoring forces, intermolecular forces, viscosity, and conservation laws.

Reactions, Processes and Experiments

Key Terms

• Stress: The internal restoring force developed per unit area of a material when it is deformed. Stress = $F/A$.
• Strain: The fractional change in dimension produced by stress. It has no unit.
• Elasticity: The property by which a material regains its original shape and size after the deforming force is removed, within its elastic limit.
• Hooke's law: Within the elastic limit, stress is directly proportional to strain.
• Young's modulus: The ratio of longitudinal stress to longitudinal strain: $Y=(F/A)/(\Delta L/L)=FL/(A\Delta L)$.
• Bulk modulus: The ratio of normal pressure increase to the resulting fractional decrease in volume: $K=-\Delta P/(\Delta V/V)$.
• Shear modulus: The ratio of tangential stress to shear strain: $G=\text{tangential stress}/\text{shear strain}$.
• Elastic limit: The greatest value of stress up to which a material returns completely to its original state when the force is removed.
• Fluid pressure: The normal force exerted by a fluid per unit area: $P=F/A$.
• Pressure at a depth: For a liquid of density $\rho$ at depth $h$, gauge pressure is $P=\rho gh$, while absolute pressure is $P_0+\rho gh$.
• Pascal's law: An externally applied pressure on an enclosed fluid is transmitted equally and undiminished in all directions.
• Atmospheric pressure: The pressure exerted by the weight of Earth’s atmosphere; standard atmospheric pressure is approximately $1.013\times 10^5\text{Pa}$.
• Buoyant force: The upward force exerted by a fluid on an immersed object, equal to the weight of the fluid displaced.
• Archimedes' principle: A body wholly or partially immersed in a fluid experiences an upward thrust equal to the weight of the fluid displaced.
• Surface tension: The tangential force per unit length acting along a liquid surface: $T=F/l$.
• Cohesive force: The attractive force between molecules of the same substance.
• Adhesive force: The attractive force between molecules of different substances.
• Angle of contact: The angle between the tangent to the liquid surface at the point of contact and the solid surface, measured through the liquid.
• Capillarity: The rise or fall of a liquid in a narrow tube due to surface tension and adhesive or cohesive forces.
• Capillary rise: For a liquid rising in a narrow tube, $h=2T\cos \theta /(\rho gr)$, where $r$ is the tube radius.
• Excess pressure in a liquid drop: For a liquid drop of radius $R$, the excess pressure is $\Delta P=2T/R$.
• Excess pressure in a soap bubble: For a soap bubble of radius $R$, the excess pressure is $\Delta P=4T/R$ because it has two surfaces.
• Viscosity: The internal friction of a fluid that opposes the relative motion of its layers.
• Coefficient of viscosity: The ratio of tangential force per unit area to velocity gradient: $\eta =(F/A)/(dv/dy)$. Its SI unit is Pa s.
• Streamline flow: A steady fluid motion in which each particle follows a smooth path and different streamlines do not cross.
• Turbulent flow: Irregular fluid motion involving eddies and rapid changes in velocity.
• Reynolds number: A dimensionless quantity used to predict flow type: $Re=\rho vd/\eta$. Low values generally indicate streamline flow, while high values indicate turbulence.
• Stokes' law: The viscous drag on a small sphere moving slowly through a fluid is $F=6\pi \eta rv$.
• Terminal velocity: The constant speed reached by a falling body in a viscous fluid when the net force on it becomes zero.
• Equation of continuity: For steady flow, mass flow rate remains constant; for an incompressible fluid, $A_1{v}_1=A_2{v}_2$.
• Bernoulli's principle: For steady, incompressible, non-viscous flow, $P+1/2\rho v^2+\rho gh$ remains constant along a streamline.

Additional essential distinctions include that stress and pressure have SI unit Pa, equal to $N{m}^{-2}$, whereas strain is dimensionless. Young's modulus, bulk modulus, shear modulus, stress, and pressure all have dimensions $[M{L}^{-1}{T}^{-2}]$. The SI unit of surface tension is $N{m}^{-1}$, equivalent to $J{m}^{-2}$, and the SI unit of coefficient of viscosity is Pa s, also written as $kg{m}^{-1}{s}^{-1}$.

Easily Confused

• Stress and strain: Stress is force per unit area, whereas strain is fractional deformation and has no unit.
• Elasticity and elastic limit: Elasticity is the property of recovery; the elastic limit is the greatest stress up to which complete recovery occurs.
• Gauge pressure and absolute pressure: Gauge pressure is $\rho gh$, whereas absolute pressure is $P_0+\rho gh$.
• Cohesive and adhesive forces: Cohesive force acts between molecules of the same substance; adhesive force acts between molecules of different substances.
• Liquid drops and soap bubbles: A liquid drop has one surface and $\Delta P=2T/R$; a soap bubble has two surfaces and $\Delta P=4T/R$.
• Streamline and turbulent flow: Streamline flow is smooth and orderly; turbulent flow contains eddies and rapid velocity changes.
• Surface tension and viscosity: Surface tension acts along a liquid surface, whereas viscosity opposes relative motion between fluid layers.
• Capillarity and viscosity: Capillarity concerns liquid rise or fall in a narrow tube; viscosity concerns internal resistance to fluid motion.
• Continuity and Bernoulli's principle: The continuity equation follows from conservation of mass, whereas Bernoulli's equation follows from conservation of mechanical energy.
• Viscosity of liquids and gases with temperature: Liquid viscosity generally decreases as temperature increases, whereas gas viscosity generally increases.
• Pressure and fluid speed in a horizontal pipe: Under Bernoulli's equation, increased fluid speed corresponds to decreased pressure.

What Gets Asked

• Define stress, strain, elasticity, elastic limit, and Hooke's law; marks are lost by treating stress and strain as interchangeable or assigning a unit to strain.
• Derive or apply $Y=(F/A)/(\Delta L/L)=FL/(A\Delta L)$, $K=-\Delta P/(\Delta V/V)$, and $G=\text{tangential stress}/\text{shear strain}$; marks are lost by using the wrong type of stress or strain.
• Calculate pressure at depth using $P=\rho gh$ or $P_0+\rho gh$; marks are lost by confusing gauge pressure with absolute pressure.
• Apply Pascal's law to an ideal hydraulic lift using $F_1/A_1=F_2/A_2$; marks are lost by failing to match each force with its corresponding piston area.
• Distinguish cohesive and adhesive forces using water rising in clean glass capillaries and mercury being depressed; marks are lost by reversing which force dominates in each case.
• Compare excess pressure in a liquid drop, $\Delta P=2T/R$, with that in a soap bubble, $\Delta P=4T/R$; marks are lost by omitting the factor of two arising from the bubble’s two surfaces.
• Classify flow using $Re=\rho vd/\eta$, and distinguish streamline flow from turbulent flow; marks are lost by associating low Reynolds numbers with turbulence.
• Apply Stokes' law and terminal velocity, including $F=6\pi \eta rv$ and $v_t=2r^2({\rho }_s-{\rho }_f)g/(9\eta )$; marks are lost by using these relations outside the stated conditions for slow motion and Stokes' law.
• Use $A_1{v}_1=A_2{v}_2$ and Bernoulli's equation; marks are lost by forgetting that, in a horizontal pipe, increased speed corresponds to decreased pressure or by ignoring the ideal-fluid assumptions.