Revision: Properties of Solids and Liquids JEE Main Properties of Solids and Liquids

The strain is defined as the ratio of change in dimensions of the body to its original dimensions.

Strain = `"change in dimensions"/"original dimensions"`

Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.

The internal restoring force per unit area of a body is called stress.

The modulus of elasticity of a material is the ratio of stress to the corresponding strain. It is defined as the slope of the stress-strain curve in the elastic deforming region and depends on the nature of the material.

\[\frac {stress}{strain}\] = Constant

The constant is called the modulus of elasticity.

In case of some materials like vulcanized rubber, when the stress applied on a body decreases to zero, the strain does not return to zero immediately. The strain lags behind the stress. This lagging of strain behind the stress is called elastic hysteresis.

A graph drawn by taking tensile strain along the x-axis and tensile stress along the y-axis, obtained by gradually increasing the load on a metal wire suspended vertically from a rigid support until the wire breaks, and measuring the elongation produced during each step.

"Young’s modulus is the ratio of longitudinal stress to longitudinal strain."

"Young’s modulus is the ratio of longitudinal stress to longitudinal strain."

"Shear modulus or modulus of rigidity: It is defined as the ratio of shear stress to shear strain within elastic limits."

"Bulk modulus is defined as the ratio of volume stress to volume strain."

Within elastic limit, the ratio of lateral strain to the linear strain is called the Poisson's ratio.

SI unit of pressure is the pascal (Pa) or Nm⁻²
One Pascal: When a force of one newton acts normally on an area of one square metre (1 m²) then the pressure acting on the surface acting on the surface is called one Pascal.

The maximum constant velocity acquired by a body while falling freely through a viscous medium is called the terminal velocity V_T.

The coefficient of viscosity of a liquid is defined as the viscous force acting tangentially per unit area of a liquid layer having a unit velocity gradient in a direction perpendicular to the direction of flow of the liquid.

The rate of change of velocity (dv) with distance (dx) measured from a stationary layer is called velocity gradient.

∴ Velocity gradient = `(dv)/dx`

When a liquid is in contact with a solid, the angle between the tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called the angle of contact.

Surface tension is defined as the force per unit length acting at right angles to an imaginary line drawn on the free surface of the liquid. 

The angle between tangents drawn at the point of contact to the liquid surface and the solid surface inside the liquid is called the angle of contact for a pair of solid and liquid. It is denoted by θ.

Surface tension is defined as the force acting on a unit length of an imaginary line drawn on the free surface of the liquid, the direction of the force being perpendicular to the line so drawn and acting parallel to the surface.

The potential energy is greater for molecules at the surface film as compared to molecules well inside the liquid. This extra energy of the molecule on the surface layer of a liquid is called the surface energy of the liquid.

"Temperature is a physical quantity that defines the thermodynamic state of a system."

One mole of any substance is the amount of that substance which contains the Avogadro number (NA) of particles (such as atoms or molecules).

"Heat is energy in transit. When two bodies at different temperatures are brought in contact, they exchange heat."

When two bodies at different temperatures are brought into contact through a diathermic wall, heat flows from the hotter body to the cooler one. This continues until both reach the same temperature, at which point heat flow stops. This state is called thermal equilibrium.

Thermometry is the branch of physics dealing with temperature measurement. It relies on the principle that certain physical properties of materials change continuously and predictably with temperature.

An adiabatic wall is an ideal partition that completely prevents heat transfer between two systems. In diagrams, it is shown as a thick, cross-hatched (slanting lines) region.

A diathermic wall is a partition that freely allows heat to flow between two systems. It is shown as a thin dark line in diagrams. A thin copper sheet is a good example.

A hypothetical gas whose molecules have no volume and exert no intermolecular forces; obeys PV = μRT exactly.

The lowest theoretically possible temperature (0 K = −273.15 °C), where ideal gas molecules have zero kinetic energy.

The SI absolute temperature scale starting at absolute zero. Written as K (no degree symbol °).

Extending a graph line beyond the measured data to predict values.

One kelvin = 1/273.16 of the difference between absolute zero and the triple point of water.

A constant in the ideal gas equation; R = 8.31 J mol⁻¹ K⁻¹.

The unique temperature & pressure at which solid, liquid, and gas phases of a substance coexist in equilibrium.

The increase in the dimensions (length, area, or volume) of a body due to an increase in its temperature is called thermal expansion. Conversely, a decrease in temperature causes contraction.

1. Consider a metallic rod of length l₀ fixed between two rigid supports at T °C.
2. If the temperature of rod is increased by ΔT, length of the rod would become, l = l₀ (1 + αΔT) Where, α is the coefficient of linear expansion of the material of the rod.
3. But the supports prevent the expansion of the rod. As a result, rod exerts stress on the supports. Such stress is termed as thermal stress.

The heat capacity of a body is the quantity of heat required to raise its temperature by 1°C. It depends upon the mass and the nature of the body.

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of unit mass of that substance through 1°C (or 1 K).

OR

Heat capacity of a body when expressed for the unit mass is called the specific heat capacity of the substance of that body.

OR

The amount of heat energy required to raise the temperature of a unit mass of an object by 1 °C is called the specific heat of that object.

Calorimetry is the science of measuring heat exchange during physical or chemical processes. The word comes from the Latin calor (heat) + Greek metron (measure).

A calorimeter is a cylindrical vessel which is used to measure the amount of heat gained (or lost) by a body when it is mixed with another body or substance.

The quantity of heat required to convert unit mass of a substance from its liquid state to vapour state, at its boiling point without any change in its temperature is called its latent heat of vapourization (L_v).

The quantity of heat required to convert unit mass of a substance from its solid state to the liquid state, at its melting point, without any change in its temperature, is called its latent heat of fusion (L_f).

OR

The heat energy absorbed at constant temperature during the transformation of solid into liquid is called the latent heat of fusion. The amount of heat energy absorbed at constant temperature by unit mass of a solid to convert into liquid phase is called the specific latent heat of fusion.

The heat energy absorbed (or liberated) in change of phase is not externally manifested by any rise or fall in temperature, it is called the latent heat.

OR

Latent heat is the quantity of heat energy required to change the state of unit mass of a substance from one phase to another, at constant temperature and constant pressure.

The coefficient of thermal conductivity of a material is defined as the quantity of heat that flows in one second between the opposite faces of a cube of side 1 m, the faces being kept at a temperature difference of 1°C (or 1 K).

Solid substances that conduct heat easily are called good conductors of heat.

Conduction is the process by which heat flows from the hot end to the cold end of a solid body without any net bodily movement of the particles of the body.

Substances that do not conduct heat easily are called bad conductors of heat.

Convection is the process by which heat is transmitted through a substance from one point to another due to the actual bodily movement of the heated particles of the substance.

The transfer of heat energy from one place to another via emission of EM energy (in a straight line with the speed of light) without heating the intervening medium is called radiation.

The heating-up of the earth’s atmosphere due to trapped infrared rays reflected from the earth's surface by atmospheric gases is called the greenhouse effect.

The mathematical expression for Young's modulus (Y) is:

Y = \[\frac{MgL}{\pi r^2l}\]

Where:

• Y = Young’s Modulus
• M = Mass of the load attached
• g = Acceleration due to gravity
• L = Original length of the wire
• r = Radius of the wire cross-section
• l = Extension or elongation produced in the wire

The mathematical expression for Young's modulus (Y) is:

Y = \[\frac{MgL}{\pi r^2l}\]

Where:

• Y = Young’s Modulus
• M = Mass of the load attached
• g = Acceleration due to gravity
• L = Original length of the wire
• r = Radius of the wire cross-section
• l = Extension or elongation produced in the wire

The formula for modulus of rigidity is:

η = \[\frac{\text{Shear Stress}}{\text{Shear Strain}}=\frac{F/A}{\theta}=\frac{F}{A\cdot\theta}\]

Where:

• η = Modulus of rigidity (Pa or N/m²)
• F = Tangential force applied (N)
• A = Cross-sectional area on which force acts (m²)
• θ = Shear strain = Δl/l (in radians)
• Δl = Displacement of the upper surface relative to the lower surface (m)
• l = Original height of the block (m)

SI Unit: Pascal (Pa) or N/m²​

Dimensional Formula: M¹L⁻¹T⁻²

The mathematical representation of Bulk Modulus (K) is:

K = \[\frac{\text{Volume Stress}}{\text{Volume Strain}}\]

K = \[\frac{dP}{\left(\frac{dV}{V}\right)}\] = V \[\frac {dP}{dV}\]

Where:

• K: Bulk Modulus
• dP: Change in pressure (Volume Stress)
• dV: Change in volume
• V: Original volume

\[\sigma=\frac{\text{Lateral strain}}{\text{Linear strain}}=\frac{\frac{d}{D}}{\frac{\Delta l}{l}}=\frac{d\cdot l}{D\cdot\Delta l}\]

Where:

• σ = Poisson's ratio
• l = original length of the wire
• ∆l = increase or decrease in length of the wire
• D = original diameter of the wire
• d = corresponding change in diameter of the wire

Important Note: Poisson's ratio has no unit. It is dimensionless.

\[E_k=\frac{3}{2}k_BT\]

Where:

• E_k = Average kinetic energy of the molecules (in joules)
• k_B = Boltzmann constant = 1.380649 × 10⁻²³ J/K
• T = Absolute temperature (in kelvin)

Q = mcΔT

Where:

• Q = Heat absorbed or released (in joules)
• m = Mass of the substance (in kg)
• c = Specific heat capacity (J/kg·K)
• ΔT = Change in temperature (T_final−T_initial)

Master Conversion Formula:

\[\frac{T_F-32}{180}=\frac{T_C}{100}\] = \[\frac {T_K−273.15}{100}\]

Master Conversion Formula:

\[\frac {T_C}{100}\] = \[\frac {(T_{F}-32)}{180}\] = \[\frac {(T_{K}-273.15)}{100}\]

Specific heat capacity c = \[\frac{\text{Heat capacity of body } C'}{\text{Mass of the body } m}\]

or

Specific heat capacity c = \[\frac{Q}{m\times\Delta t}\]

Q = m × L

where,

Q = Heat energy absorbed or released during phase change
m = Mass of the substance undergoing phase change
L = Specific Latent Heat (characteristic of the substance & process)

SI Units = J kg⁻¹

Proportionality Form

\[\frac{dT}{dt}\propto(T-T_0)\]

Introducing the constant of proportionality C:

\[\frac{dT}{dt}=C\left(T-T_0\right)\]

T = Temperature of the body at time t
T₀ = Temperature of the surroundings (constant)
C = Constant of proportionality
\[\frac {dT}{dt}\] = Rate of fall of temperature (rate of cooling)

T = `F/L`

where F = Force (N), L = Length (m)

= SI unit of T = `N/m`

Surface tension can also be written as

T = `W/A`

where W = Work (J), A = Area (m²)

= SI unit of T = `J/m^2`

We know

1J=1N×1m

So,

`J/m^2 = (N * m)/m^2 = N/m`

Both units are the same

`1N/m equiv 1J/m^2`

If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.

"The rate of loss of heat (dT/dt) of a body is directly proportional to the difference in temperatures (T−T₀) of the body and the surroundings, provided the difference in temperatures is small."

A hot body loses heat to its surroundings in the form of heat radiation. The rate of loss of heat depends on the difference in temperature of the body and its surroundings.​

(b) There is no gravitational force acting downwards. However, when the starting velocity is 20 m/s, the viscous force, which is directly proportional to velocity, becomes maximum and tends to accelerate the ball upwards.

\[\text{ When the ball falls under gravity, }\]

\[\text{ neglecting the density of air: } \]

\[\text{ Mass of the sphere = m }\]

\[\text{ Radius = r }\]

\[\text{ Viscous drag coeff . }= \eta\]

\[\text{Terminal velocity is given by}: \]

\[\text{ mg  }= 6\pi\eta r v_T \]

\[ \Rightarrow \frac{6\pi\eta r v_T}{m} = g . . . (1)\]

\[\text{ Now, at terminal velocity, the acceleration of the ball due to the viscous force is given by: } \]

\[a = \frac{6\pi\eta r v_T}{m}\]

\[\text{ Comparing equations (1) and (2), we find that : } \]

\[ \text{ a = g }\]

Thus, we see that the initial acceleration of the ball will be 9.8 ms - 2  .

(c) The velocity of the ball will decrease with time because of the upward viscous drag. As the force of viscosity is directly proportional to the velocity of the ball, the acceleration due to the viscous force will also decrease.

(d) When all the kinetic energy of the ball is radiated as heat due to the viscous force, the ball comes to rest. 

• Gases expand linearly with temperature, making them useful for thermometers. This consistent behaviour suggests the existence of a lowest temperature limit.
• Absolute zero (−273.15 °C or 0 K) is the temperature where an ideal gas would have zero pressure. It is the lowest possible temperature.
• The Kelvin scale begins at absolute zero and uses the triple point of water (273.16 K) as a reference point. It is the SI temperature scale.
• The ideal gas equation (PV = μRT) combines all gas laws into a single relationship among pressure, volume, and temperature. It works best for gases at low pressure and high temperature.

• Heat energy absorbed (Q) depends on: mass (m), rise in temperature (Δt), and specific heat capacity (c), i.e., Q ∝ m × Δt × c.
• Heat capacity (C') and specific heat capacity (c) are related by: C′ = m × c.

• Calorimeter: An insulated device used to measure heat transfer during a process.
• Principle of Calorimetry: Heat lost = Heat gained (energy is conserved).
• Method of Mixtures: Heat a sample, place it in the calorimeter, and measure the temperature change to calculate the heat.
• Formula: Used to calculate the specific heat of a substance from measured temperatures and masses.
• Good Practice: Transfer the sample quickly and stir well for accurate results.
• Why Water is Used: Water has high specific heat, so it absorbs a lot of heat without a large temperature change.

• Formula: Q = mL. Specific latent heat L has SI unit J kg⁻¹.
• Temperature stays constant during any phase change. Heat energy goes into breaking or forming intermolecular bonds, not into raising kinetic energy.
• Latent Heat of Fusion (water): L_f = 3.33 × 10⁵ J kg⁻¹ = 80 cal/g. Heat needed to melt 1 kg of ice at 0°C.
• Latent Heat of Vaporisation (water): L_v = 22.6 × 10⁵ J kg⁻¹ = 540 cal/g. Heat is needed to convert 1 kg of water to steam at 100°C.
• L_v ≫ L_f because vaporisation requires complete molecular separation and work against atmospheric pressure during expansion.
• All latent heat values depend on atmospheric pressure. Standard values quoted at 1 atm. Increasing pressure raises the boiling point (pressure cooker effect).

• Heat can be transferred in three ways — conduction, convection, and radiation.
• Conduction transfers heat through solids; molecules vibrate but do not move from their positions.
• Convection transfers heat through liquids and gases; molecules physically move from place to place.
• Both conduction and convection require a material medium; radiation does not.
• Radiation travels through electromagnetic waves at a speed of 3×10⁸ ms⁻¹.
• Conduction is the slowest process, convection is rapid, and radiation is the fastest mode of heat transfer.
• The energy received from the Sun is an example of heat transfer by radiation.

• The transfer of heat from the hot part to the cold part of an object is called conduction of heat.
• Conduction takes place through solid substances only — it requires a medium.
• Heat travels by molecular collisions: fast-vibrating molecules pass energy to slower neighbours.
• Copper conducts heat faster than aluminium, which conducts faster than steel.
• Conduction of heat through a substance depends on the property of that substance.
• Good conductors: silver, copper, aluminium, brass — all metals.
• Bad conductors: wood, cloth, air, paper — most non-metals.
• Good conductors of heat are also good conductors of electricity, and bad conductors of heat are also bad conductors of electricity.

• Convection occurs only in fluids (liquids and gases) — not in solids.
• In conduction, molecules vibrate but stay in place.
• In convection, molecules physically move from one place to another.
• Heating reduces density → hot fluid rises; cool fluid sinks → a convection current is set up.
• Convection currents transfer heat to the entire mass of the fluid.
• Potassium permanganate makes convection currents visible as magenta-coloured streams.

• When water is heated from the top, its density decreases, and it stays at the top. Since hot water cannot sink, convection does not occur and the bottom remains cool.
• Radiation is the transfer of heat without a medium — through electromagnetic waves.
• Heat from the Sun reaches us through radiation across the vacuum of space.
• All objects above 0 K emit thermal radiation (electromagnetic waves).
• Radiation is a two-step process: thermal energy → EM waves → thermal energy.
• Black or dark surfaces absorb more heat radiation; absorption also depends on the intrinsic properties of the substance.
• An infrared camera uses the radiation emitted by objects to see at night — useful for military surveillance.
• Copper is an excellent conductor; plastic is a bad conductor (insulator).
• Heat readily conducts through metals (copper and steel) but not through non-metals (wood and plastic).

• A hot body loses heat to its surroundings in the form of heat radiation.​
• The rate of cooling is directly proportional to the temperature difference between the body and its surroundings.
• The cooling curve (T vs t) shows rapid initial cooling that gradually slows down.
• Plotting \[\frac {dT}{dt}\] vs (T−T₀) gives a straight line through the origin, confirming Newton's law.​
• Mathematically: dT/dt = C(T − T₀), where C is the constant of proportionality.​
• The rate of cooling is proportional to — not independent of — the temperature difference. A 4× drop in temperature difference produces a 4× drop in cooling rate.