Properties of Solids and Liquids – JEE Mains Physics
1. Elastic Behaviour and Stress-Strain Relationship
- Elastic behaviour refers to the ability of a material to return to its original shape after the removal of a deforming force.
- Stress-Strain Relationship describes how materials deform under applied forces.
- Formula for Stress (σ) and Strain (ϵ):
σ = F / A, ϵ = ΔL / L₀
where F is the force, A is the cross-sectional area, ΔL is the change in length, and L₀ is the original length.
2. Hooke’s Law
- Hooke’s Law states that the strain in a solid is proportional to the applied stress within the elastic limit.
- Formula:
F = kx
where F is the force, k is the spring constant, and x is the displacement.
3. Young’s Modulus
- Young’s Modulus (Y) is a measure of the stiffness of a solid material.
- Formula:
Y = (Stress / Strain) = (F / A) / (ΔL / L₀) = (FL₀) / (AΔL)
4. Bulk Modulus
- Bulk Modulus (B) describes the material's response to uniform pressure applied in all directions.
- Formula:
B = - (ΔP / ΔV) * V
where ΔP is the change in pressure, and ΔV is the change in volume.
5. Modulus of Rigidity
- Modulus of Rigidity (G) is a measure of the material's response to shear stress.
- Formula:
G = (Shear Stress / Shear Strain) = (F / A) / (x / L)
6. Pressure Due to a Fluid Column
- Pressure at a point in a fluid is given by:
P = ρgh
where ρ is the fluid density, g is acceleration due to gravity, and h is the height of the fluid column.
7. Pascal’s Law and Its Applications
- Pascal’s Law states that any change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
- Applications: Hydraulic presses, car lifts, etc.
8. Viscosity
- Viscosity is the measure of a fluid’s resistance to flow.
- Formula for Viscosity (η):
η = (F * L) / (A * v)
where F is the force, L is the length, A is the area, and v is the velocity of the fluid flow.
9. Stoke’s Law and Terminal Velocity
- Stoke’s Law describes the force of viscosity on a spherical object moving through a fluid.
- Formula:
F = 6πηrv
where η is the fluid viscosity, r is the radius of the sphere, and v is the velocity of the sphere. - Terminal Velocity is the constant velocity a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.
10. Streamline and Turbulent Flow
- Streamline Flow: Fluid moves in parallel layers with no disruption between them.
- Turbulent Flow: Irregular and chaotic flow of fluid with eddies and vortices.
- Critical Velocity is the velocity at which the flow of the fluid changes from laminar to turbulent.
11. Bernoulli’s Principle and Its Applications
- Bernoulli’s Principle states that for an incompressible, non-viscous fluid, the total mechanical energy (pressure energy, kinetic energy, and potential energy) remains constant along a streamline.
- Formula:
P + ½ρv² + ρgh = constant
- Applications: Airplane wings, fluid dynamics in pipes, etc.
12. Surface Energy and Surface Tension
- Surface Tension is the force acting at the surface of a liquid, causing it to behave like a stretched elastic membrane.
- Surface Energy is the energy required to increase the surface area of a liquid.
13. Angle of Contact and Excess Pressure
- Angle of contact is the angle formed between the tangent to the surface of the liquid and the solid surface.
- Excess Pressure across a curved surface:
P = 2T / r
where T is the surface tension, and r is the radius of curvature.
14. Applications of Surface Tension
- Applications include drops, bubbles, and capillary rise.
15. Heat, Temperature, and Thermal Expansion
- Heat is the energy transferred between bodies at different temperatures.
- Temperature is a measure of the average kinetic energy of particles in a substance.
- Thermal Expansion describes the change in the dimensions of a material when heated.
16. Specific Heat Capacity and Calorimetry
- Specific Heat Capacity (c) is the amount of heat required to change the temperature of 1 kg of a substance by 1°C.
- Calorimetry is the science of measuring the heat of chemical reactions or physical changes.
17. Change of State and Latent Heat
- Latent Heat is the heat required to change the state of a substance without changing its temperature.
18. Heat Transfer: Conduction, Convection, and Radiation
- Conduction: Transfer of heat through a material without the movement of the material itself.
- Convection: Transfer of heat by the movement of fluids (liquids or gases).
- Radiation: Transfer of heat through electromagnetic waves.