Angle of Contact in Surface Tension Definition, Formula and Examples – Physics

Define Angle of Contact:
The angle subtended between the tangents drawn at liquid surface and at the solid surface inside the liquid at the point of contact is called angle of contact (θ).

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Angle of Contact in Physics | Definition – Surface Tension

If liquid molecules is in contact with solid (i.e. wall of capillary tube), then forces acting on liquid molecules are
(i) Force of cohesion Fc (acts at an angle 45° to the vertical)
(ii) Force of adhesion Fa (acts outwards at right angle to the wall of the tube)
Angle of Contact

Angle of contact depends upon the nature of the liquid and solid in contact and the medium which exists above the free surface of the liquid.

When wax is coated on a glass capillary tube, it becomes water-proof. The angle of contact increases and becomes obtuse. Water does not rise in it. Rather it falls in the tube by virtue of obtuse angle of contact.

  • If θ is acute angle, i.e. θ<9o°, then liquid meniscus will be concave upwards.
  • If θ is 90°, then liquid meniscus will be plane.
  • If θ is obtuse, i.e. θ>9o°, then liquid meniscus will be convex upwards.
  • If angle of contact is acute angle, i.e. θ<9o°, then liquid will wet the solid surface.
  • If angle of contact is obtuse angle, i.e. θ>90°, then liquid will not wet the solid surface.

Angle of contact increases with increase in temperature of liquid. Angle of contact decreases on adding soluble impurity to a liquid.

  • Angle of contact for pure water and glass is zero.
  • For ordinary water and glass, it is 8°.
  • For mercury and glass, it is 138°.
  • For pure water and silver, it is 90°.
  • For alcohol and clean glass θ = 0°.

Angle of Contact, Meniscus, and Shape of liquid surface

Angle Of Contact In Surface Tension

Surface Tension:
In Physics, the tension of the surface film of a liquid because of the attraction of the surface particles by the bulk of the liquid, which tries to minimize surface area is called surface tension. When the surface of the liquid is strong enough, then surface tension is applicable. It is strong enough to hold weight.

Surface Tension Adhesive Force
Cohesive Force Molecular Range
Factors Affecting Surface Tension Surface Energy
Angle of Contact Capillarity
Jurin’s Law

Kinetic Theory of Ideal gases | Properties – Kinetic Theory of Gases

Kinetic Theory of Ideal Gases:
Kinetic theory of gases explains the behavior of gases, it correlates the macroscopic properties of gases e.g., Pressure, temperature etc., to the microscopic properties like speed, momentum, kinetic energy etc.

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Kinetic Theory of Ideal gases | Properties – Kinetic Theory of Gases

Kinetic theory of gases, a theory based on a simplified molecular or particle description of a gas, from which many gross properties of the gas can be derived.

Microscopic and Macroscopic Properties in Thermodynamics:

Macroscopic Properties of Gases:

  • Volume,
  • Pressure, and
  • Temperature

Microscopic Properties of Gases:

  • speed,
  • momentum,
  • kinetic energy, etc.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Critical Temperature, Pressure and Volume – Kinetic Theory of Gases

Critical Temperature, Pressure and Volume – Kinetic Theory of Gases

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Critical Temperature, Pressure and Volume
Gases can’t be liquified above a temperature called critical temperature (TC) however large the pressure may be.

The critical temperature of a substance is the temperature at and above which vapor of the substance cannot be liquefied, no matter how much pressure is applied.

Critical Pressure Definition:
The pressure required to liquify the gas at critical temperature is called critical pressure (pC)
The critical pressure is the vapor pressure of a fluid at the critical temperature above which distinct liquid and gas phases do not exist.

Critical Volume Physics Definition:
The volume of the gas at critical temperature and pressure is called critical volume (VC).
The volume occupied by a certain mass, usually one gram molecule of a liquid or gaseous substance at its critical point: The numerical value of the critical volume depends upon the amount of gas under experiment.

Value of critical constants in terms of van der Waals’ constants a and b are as under

VC = 3b, pC = \(\frac{a}{27 b^{2}}\) and TC = \(\frac{8 a}{27 R b}\)

Further, \(\frac{R T_{C}}{p_{C} V_{C}}=\frac{8}{3}\) is called critical coefficient and is same for all gases.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

What is the Ideal Gas Law? | Definition, Formula, Units – Kinetic Theory of Gases

Ideal or Perfect Gas Equation:
Perfect gas also called an ideal gas. Gases which obey all gas laws in all conditions of pressure and temperature are called perfect gases.

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What is the Ideal Gas Law? | Definition, Formula, Units – Kinetic Theory of Gases

In most usual conditions (for instance at standard temperature and pressure), most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases.

Ideal Gas Law Formula:
Ideal Gas Law or Equation of perfect gas

PV = nRT

where,
P = pressure,
V = volume,
T = absolute temperature,
R = universal gas constant and
n = number of moles of a gas.
Universal gas constant, R = 8.31 J mol-1K-1.

Ideal Gas Equation Units:
In SI units, p is measured in pa or N/m²
V is measured in cubic metres, (m³)
n is measured in moles, and
T in kelvins

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Kinetic Theory of Gases Assumptions – Kinetic Theory of Gases

Kinetic Theory of Gases Assumptions – Kinetic Theory of Gases

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Assumptions of Kinetic Theory of Gases:
1. Every gas consists of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from those of another gas.

2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.

3. Their molecular size is negligible in comparison to intermolecular distance (10-9m).

4. The speed of gas molecules lies between zero and infinity (very high speed).

5. The distance covered by the molecules between two successive collisions is known as free path and mean of all free path is known as mean free path.

6. The number of collisions per unit volume in a gas remains constant.

7. No attractive or repulsive force acts between gas molecules.

8. Gravitational attraction among the molecules is ineffective due to extremely small masses and very high speed of molecules.

9. The density of gas is constant at all points of the vessel.

10. The molecules of a gas keep on moving randomly in all possible directions with all possible velocities.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

What is Brownian Motion in Physics? | Definition, Examples – Kinetic Theory of Gases

Brownian Motion Simple Definition:
The continuous random motion of the particles of microscopic size suspended in air or any liquid is called Brownian motion.

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What is Brownian Motion in Physics? | Definition, Examples – Kinetic Theory of Gases

Brownian motion is observed with many kind of small particles suspended in both liquids and gases.

Brownian motion is due to the unequal bombardment of the suspended particles by the molecules of the surrounding medium.

Brownian Motion Examples

  • The motion of pollen grains on still water.
  • Movement of dust motes in a room (although largely affected by air currents)
  • Diffusion of pollutants in the air.
  • Diffusion of calcium through bones.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Mean Free Path Physics | Definition, Formula – Kinetic Theory of Gases

Mean Free Path Definition Physics:
The average distance travelled by a molecule between two successive collisions is called mean free path (λ).

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Mean Free Path Physics | Definition, Formula – Kinetic Theory of Gases

Mean Free Path Formula Physics:
Mean free path is given by

λ = \(\frac{k T}{\sqrt{2} \pi \sigma^{2} p}\)

Mean Free Path
where,
σ = diameter of the molecule,
p = pressure of the gas,
T = temperature and
k = Boltzmann’s constant.

Mean free path, λ ∝ T and

Mean Free Path is Inversely Proportional to,

λ ∝ \(\frac{1}{p}\)

Mean Free Path in Kinetic Theory of Gases

On the basis of kinetic theory of gases, it is assumed that the molecules of a gas are continuously colliding against each other. Mean Free Path is the average distance traversed by molecule between two successive collisions.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Degrees of Freedom in Physics | Definition, Formula – Kinetic Theory of Gases

Degrees of Freedom in Physics Definition:
The degree of freedom for a dynamic system is the number of directions in which a particle can move freely or the total number of coordinates required to describe completely the position and configuration of the system.
It is denoted by f or N.

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Degrees of Freedom in Physics | Definition, Formula – Kinetic Theory of Gases

Degrees of Freedom Formula Physics:
Suppose if we have A number of gas molecules in the container, then the total number of degrees of freedom is f = 3A. But, if the system has R number of constraints (restrictions in motion) then the degrees of freedom decreases and it is equal to f = 3A-R where A is the number of particles.
Degree of freedom of a system is given by

f or N = 3A – R

where,
A = number of particles in the system and
R = number of independent relations between the particles.

Degree of freedom for different atomic particles are given below.

  1. For monoatomic gas = 3 (all translational).
  2. For diatomic gas = 5 (3 translational, 2 rotational)
  3. For non-linear triatomic gas = 6 (3 translational, 3 rotational)
  4. For linear triatomic gas = 7 (3 translational,3 rotational and 1 vibrational)

Specific heat of a gas

(a) At constant volume, Cv = \(\frac{f}{2}\)R.
(b) At constant pressure, Cp = \(\left(\frac{f}{2}+1\right)\)R
(c) Ratio of specific heats of a gas at constant pressure and at constant volume is given by γ = 1 + \(\frac{2}{f}\)

Specific heat of solids, C = 3R ⇒ C = 24.93 Jmol-1 K-1.
Specific heat of water, C = 9R ⇒ C = 74.97 Jmol-1 K-1.
Degrees of Freedom

Maxwell’s Law or the Distribution of Molecular Speeds
It derives an equation giving the distribution of molecules at different speeds

dN = 4πN\(\left(\frac{m}{2 \pi k T}\right)^{3 / 2} v^{2} e^{-\left(\frac{m v^{2}}{2 k T}\right)} \cdot d v\)

where, dN is number of molecules with speed between v and v + dv.
The \(\frac{d N}{d v}\) versus v curve is shown below
Degrees of Freedom

Law of Equipartition of Energy

This law states that, for a dynamic system in thermal equilibrium, the total energy is distributed equally amongst all the degree of freedom and the energy associated with each molecule per degree of freedom is

\(\frac{1}{2}\) kB T.

where,
kB = 1.38 x 10-23 JK-1 is Boltzmann constant and
T is the absolute temperature of system on the kelvin scale.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Real Gases | Definition, Formula, Units – Kinetic Theory of Gases

Real Gases Definition:
Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law.
Real gases deviate slightly from ideal gas laws because

  1. Real gas molecules attract one another.
  2. Real gas molecules occupy a finite volume.

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Real Gases | Definition, Formula, Units – Kinetic Theory of Gases

Real or van der Waals’ Gas Equation
\(\left(p+\frac{a}{V^{2}}\right)\) (V – b) = RT

where, a and b are called van der Waals’ constants.

Dimension [a] = [ML5T-2] and [b] = [L3]
Units a = N-m4 and b = m3.

Note:
Real gases obey this equation at high pressure and low temperature

Pressure of a gas
Pressure due to an ideal gas is given by
p = \(\frac{1}{3} \frac{m n}{V}\)v2 = \(\frac{1}{3} \rho \bar{v}^{2}\)

For one mole of an ideal gas, where, m = mass of one molecule, n = number of molecules,

V = volume of gas, \(\bar{v}=\sqrt{\frac{\bar{v}_{1}^{2}+\bar{v}_{2}^{2}+\ldots+\bar{v}_{n}^{2}}{n}}\)
is called root mean square (rms) velocity of the gas molecules and M = molecular weight of the gas.

If p is the pressure of the gas and E is the kinetic energy per unit volume is E, then
p = \(\frac{2}{3}\)E

Note:
Effect of mass, volume and temperature on pressure

  • when volume and temperature of a gas are constant, then pressure ∝ mass of gas.
  • when mass and temperature of a gas are constant, then pressure ∝ \(\frac{1}{\text { volume }}\)
  • when mass and volume of gas are constant, then pressure ∝ temperature ∝ c2.

Kinetic Energy of a Gas and Speed of Gas Molecules

(i) Average kinetic energy of translation per molecule of a gas is given by

E = \(\frac{3}{2}\) kT

where, k = Boltzmann’s constant.

(ii) Average kinetic energy of translation per mole of a gas is given by

E = \(\frac{3}{2}\) RT

where, R = universal gas constant.

(iii) For a given gas kinetic energy

E ∝ T
⇒ \(\frac{E_{1}}{E_{2}}=\frac{T_{1}}{T_{2}}\)

(iv) Root mean square (rms) velocity of the gas molecules is given by

\(v\) = \(\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 p}{\rho}}\)

(v) For a given gas, \(v\) ∝ \(\sqrt{T}\)

(vi) For different gases, \(v\) ∝ \(\frac{1}{\sqrt{M}}\)

(vii) Boltzmann’s constant, k = \(\frac{R}{N}\)
where, R is an ideal gas constant and N = Avogadro number.
Value of Boltzmann’s constant is 1.38 × 10-28 J/K.

(viii) The average speed of molecules of a gas is given by

\(\bar{v}=\sqrt{\frac{8 k T}{\pi m}}=\sqrt{\frac{8 R T}{\pi M}}\)

(ix) The most probable speed of molecules u of a gas is given by

\(v_{\mathrm{mp}}=\sqrt{\frac{2 k T}{m}}=\sqrt{\frac{2 R T}{M}} \Rightarrow v_{\mathrm{rms}}>\bar{v}>v_{\mathrm{mp}}\)

(x) With rise in temperature rms speed of gas molecules increases as

\(v_{\mathrm{rms}}\) ∝ \(\sqrt{T}\)

(xi) With the increase in molecular weight rms speed of gas molecule decrease as

\(v_{\mathrm{rms}}\) ∝ \(\frac{1}{\sqrt{M}}\)

(xii) Rms speed of gas molecules is of the order of km/s, e.g. at NTP for hydrogen gas

\(v_{\mathrm{rms}}\) = \(\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 \times 8.31 \times 273}{2 \times 10^{3}}}\) = 1.84

(xiii) Rms speed of gas molecules does not depend on the pressure of gas (if temperature remains constant) because p ∝ ρ (Boyle’s law). If pressure is increased n times, then density will also increase by n times but υrms remains constant.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature

Gas Laws in Physics | Boyle’s Law, Charles’ Law, Gay Lussac’s Law, Avogadro’s Law – Kinetic Theory of Gases

Gas Laws physics:
Through experiments, it was established that gases irrespective of their nature obey the following laws

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Gas Laws in Physics | Boyle’s Law, Charles’ Law, Gay Lussac’s Law, Avogadro’s Law – Kinetic Theory of Gases

Boyle’s Law is represented by the equation:
At constant temperature, the volume (V) of given mass of a gas is inversely proportional to its pressure (p), i.e.
Gas Laws

V ∝ \(\frac{1}{p}\) ⇒ pV = constant

For a given gas, p1V1 = p2V2

Charles’ Law
At constant pressure, the volume (V) of a given mass of gas is directly proportional to its absolute temperature (T), i.e.

V ∝T ⇒ \(\frac{V}{T}\) = constant

For a given gas, \(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}\)

At constant pressure, the volume (V) of a given mass of a gas increases or decreases \(\frac{1}{273.15}\) by of its volume at 0°C for each 1°C rise or fall in temperature.
Image
Volume of the gas at t°C,
Vt = V0\(\left(1+\frac{t}{273.15}\right)\)

where, V0 is the volume of gas at 0°C.

Gay Lussac’s or Regnault’s Law
At constant volume, the pressure p of a given mass of gas is directly proportional to its absolute temperature T, i.e.

p ∝ T ⇒ \(\frac{P}{T}\) = constant

For a given gas, \(\frac{p_{1}}{T_{1}}=\frac{p_{2}}{T_{2}}\)

At constant volume, the pressure p of a given mass of a gas increases or decreases by \(\left(1+\frac{t}{273.15}\right)\) of its pressure at 0°C for each 1°C rise or fall in
Gas Laws

Volume of the gas at t°C,
pt = p0\(\left(1+\frac{t}{273.15}\right)\)

where, p0 is the pressure of gas at 0°C.

Avogadro’s Law
Avogadro stated that equal volume of all the gases under similar conditions of temperature and pressure contain equal number of molecules. This statement is called Avogadro’s hypothesis. According to Avogadro’s law N1 = N2, where N2 and N2 are number of molecules in two gases respectively.

(i) Avogadro’s number:
The number of molecules present in lg mole of a gas is defined as Avogadro’s number.
NA = 6.023 x 1023 per gram mole

(ii) At STP or NTP (T = 273 K and p = 1 atm), 22.4 L of each gas has 6.023 x 1023 molecules.

(iii) One mole of any gas at STP occupies 22.4 L of volume.

Dalton’s Law of Partial Pressure
It states that the total pressure of a mixture of non-interacting ideal gases is the sum of partial pressures exerted by individual gases in the mixture, i.e. p = p1 + p2 + p3 + ………

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

Kinetic Energy of an Ideal Gas Assumptions of Kinetic Theory of Gases
Gas Laws Ideal Gas Equation
Real Gases Degrees of Freedom
Mean Free Path Brownian Motion
Critical Temperature