Physics

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.

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,
V_t = 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

Volume of the gas at t°C,
p_t = 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.
N_A = 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

Triple Point of Water Definition:
The values of pressure and temperature at which water coexists in equilibrium in all three states of matter, i.e. ice, water and vapour is called triple point of water.

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What is Triple Point of Water? | Definition – Thermometry and Calorimetry

Triple point of water is 273 K temperature and 0.46 cm of mercury pressure.

The triple point of water, T₃ = 273.16 K, is the standard fixed-point temperature for the calibration of thermometers. This agreement also sets the size of the kelvin as 1/273.16 of the difference between the triple-point temperature of water and absolute zero.

Why is the Triple Point of Water Important

It is also important to note that the triple point of water correlates with the pressure necessary for liquid water to exist. Because ice is less dense than liquid water, ice frozen at pressures below the triple point will sublime directly into water vapor.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Water Equivalent Definition:
It is the quantity of water whose thermal capacity is same as the heat capacity of the body. Water equivalent is generally used in comparison of a water quantity.

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What is Water Equivalent? | Definition, Symbol, Units, Formula – Thermometry and Calorimetry

Water Equivalent Symbol:
It is denoted by W.

W = ms = heat capacity of the body.

Water Equivalent Unit:
SI unit for water is kg
Its expressed in the unit gram.

Water Equivalent Dimensional Formula:
Dimensional formula is [M¹L⁰T⁰].

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Thermal Equilibrium Definition Physics:
When there is no transfer of heat between two bodies in contact, then the bodies are called in thermal equilibrium. The objects in thermal equilibrium have the same temperature.

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Thermal Equilibrium | Definition, Examples – Thermometry and Calorimetry

Thermal Equilibrium Examples:

• The cooling object in the refrigerator
• Taking the temperature of a sick patient (Thermometer)
• Rice cooker with a thermostat
• Baking cake in an oven
• Cooling Drinks
• A wet towel is placed on the forehead of a person who has high fever.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Calorimetry Physics Meaning:
This is the branch of heat transfer that deals with the measurement of heat. The heat is usually measured in calories or kilo calories.

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Principle of Calorimetry | Definition – Thermometry and Calorimetry

Calorimetry is the science or act of measuring changes in state variables of a body for the purpose of deriving the heat transfer associated with changes of its state.

Principle of Calorimetry:
When a hot body is mixed with a cold body, then heat lost by hot body is equal to the heat gained by cold body.

Heat lost = Heat gain

i.e. principle of calorimetry follows the law of conservation of heat energy.

If two substances having masses m₁ and m₂, specific heats c₁, and c₂ kept at temperatures T₁ and T₂ (T₁ >T₂) are mixed, such that temperature of mixture at equilibrium is T_mix.
Then,
m₁.c₁(T₁ – T_mix) = m₂c₂(T_mix – T₂)

or

T_mix = \(\frac{m_{1} c_{1} T_{1}+m_{2} c_{2} T_{2}}{m_{1} c_{1}+m_{2} c_{2}}\)

Temperature of Mixture in Different Cases

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Joule’s Law 
According to Joule, whenever heat is converted into work or work is converted into heat, then the ratio of between work and heat in constant.

\(\frac{W}{Q}\) = J

where J is the mechanical equivalent of heat.

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Joule’s Law of Heating | Definition of Joule’s Law – Thermometry and Calorimetry

When water falls from height h, then increase in temperature dT at the bottom is

dT = \(\left(\frac{g h}{J \cdot C}\right)^{\circ} \mathrm{C}\)

• When m kg of ice-block falls from height h and its some part m’ is melt down, then

h = \(\frac{m^{\prime}}{m}\left(\frac{J L}{g}\right)\) meter

If ice-block melts completely, then m = m’ and hence h = \(\frac{J L}{g}\)

“Joule’s first law” (Joule heating), a physical law expressing the relationship between the heat generated and current flowing through a conductor.

“Joule’s second law” states that the internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature.

Melting
Conversion of solid into liquid state at constant temperature is called melting.

Fusion and Freezing Point
The process of change of state from liquid to solid is called fusion. The temperature at which liquid starts to freeze is known as the freezing point of the liquid.

Evaporation
Conversion of liquid into vapour at all temperatures (even below its boiling point) is called evaporation.

Boiling
When a liquid is heated gradually, at a particular temperature the saturated vapour pressure of the liquid becomes equal to the atmospheric pressure, now bubbles of vapour rise to the surface of the liquid. This process is called boiling of the liquid.

The temperature at which liquid boils is called boiling point.

The boiling point of water increases with increase in pressure and decreases with decrease in pressure.

Sublimation
The conversion of a solid into vapour state is called sublimation.

Hoar Frost
The conversion of vapours into solid state is called hoar frost.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Latent Heat Definition: (Change of State)
The heat energy absorbed or released at constant temperature per unit mass for change of state is called latent heat.

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Latent Heat | Definition, Formula, Units – Thermometry and Calorimetry

Latent Heat Formula Physics:
Heat energy absorbed or released during change of state is given by

Q = mL

where,
m = mass of the substance and
L = latent heat

Latent Heat Unit:
Its unit is cal/g or J/kg

Latent Heat Dimensional Formula:
Dimensional formula is [L² T^-2].

Latent Heat of Vaporization of Water:
For water at its normal boiling point or condensation temperature (100°C), the latent heat of vaporization is

L = 540 cal/g = 40.8 kJ/ mol
= 2260 kJ/kg

Latent Heat of Fusion of Water:
For water at its normal freezing temperature or melting point (0°C), the latent heat of fusion is

L = 80 cal/ g = 60 kJ/mol
= 336 kJ/kg

It is more painful to get burnt by steam rather than by boiling water at 100°C. Steam converted to water at 100°C, then it gives out 536 cal of heat, so, it is clear that steam at 100°C has more heat than water at 100°C (i.e. boiling of water).

After snow falls, the temperature of the atmosphere becomes very low. This is because the snow absorbs the heat from the atmosphere to melt down. So, in the mountains, when snow falls, one does not feel too cold but when ice melts, he feels too cold.

There is more shivering effect of icecream on teeth as compared to that of water (obtained from ice). This is because when icecream melts down, it absorbs large amount of heat from teeth.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Thermal Capacity Definition Physics: (Heat) Capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature.

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Thermal (Heat) Capacity | Definition, Formula, Units – Thermometry and Calorimetry

Thermal Capacity Formula:
Heat capacity of any body is equal to the amount of heat energy required to increase its temperature through 1°C.

Heat capacity = mc

where, c = specific heat of the substance of the body and m = mass of the body.

Thermal Capacity Unit:
Its SI unit is joule/kelvin (J/K)

Thermal Capacity Dimensional Formula:
Dimensional formula [ML²T^-2K^-1].

Molar Specific Heat Capacity Formula:
Molar specific heat capacity,

c = \(\frac{s}{\mu}=\frac{\Delta Q}{\mu \Delta T}\)

where, µ = number of moles of substances (gas).

The relation between c and M are

c = MS

where,
M = molecular mass of substance and
S = specific heat capacity.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Specific Heat Definition:
The amount of heat required to raise the temperature of unit mass of the substance through 1°C is called its specific heat.

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What is Specific Heat Capacity? | Definition, Units, Types – Thermometry and Calorimetry

Specific Heat Symbol:
It is denoted by c or s.

Specific Heat Unit:
Its SI unit is ‘joule/kilogram-°C’ (J/kg-°C) or Jkg^-1K^-1

Dimensional Formula of Specific Heat:
The dimensional formula is [L²T²θ^-1].

Specific Heat of Water:
The specific heat of water is 4200 J kg^-1°C^-1 or 1 cal g^-1 C^-1 which is high as compared with most other substances.

Specific Heat Capacity Formula:
The amount of heat energy required to change the temperature of any substance is given by

Q = mcΔt

where,
m = mass of the substance,
c = specific heat of the substance and
Δt = change in temperature

Gases have two types of specific heat

1. The specific heat capacity at constant volume (C_v).
2. The specific heat capacity at constant pressure (C_p).

Specific heat at constant pressure (C_p) is greater than specific heat at constant volume (C_v), i.e. C_p>C_v.
For molar specific heats, C_p – C_v = R
where, R = gas constant and this relation is called Mayer’s formula.

The ratio of two principal sepecific heats of a gas is represented by γ, i.e.

γ = \(\frac{C _{p}}{C_{V}}\)

The value of γ depends on atomicity of the gas.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry

Thermal Expansion Definition:
When matter is heated without any change in its state, it usually expand. This phenomena of expansion of matter on heating, is called thermal expansion.

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Thermal Expansion in Physics | Definition, Types, Applications – Thermometry and Calorimetry

Thermal Expansion Types:
There are three types of thermal expansion

• Expansion of Solids
• Expansion of Liquids
• Thermal Expansion of Gases

1. Expansion of Solids
Three types of expansion takes place in solid

(i) Linear Expansion:
Expansion in length on heating is called linear expansion.
Increase in length,

l₂ = l₁ (1 + α Δt)

where, l₁, and l₂ are initial and final lengths, Δt = change in temperature and α = coefficient of linear expansion.

Coefficient of linear expansion,

α = \(\frac{\Delta l}{l \times \Delta t}\)

where, l =real length and Δl = change in length and Δt = change in temperature.

(ii) Superficial Expansion:
Expansion in area on heating is called superficial expansion.
Increase in area,

A₂ = A₁ (1 + β Δt)

where, A₁ and A₂ are initial and final areas and β is a coefficient of superficial expansion.

Coefficient of superficial expansion,

β = \(\frac{\Delta A}{A \times \Delta t}\)

where, A = area, ΔA = change in area and Δt = change in temperature.

(iii) Cubical Expansion:
Expansion in volume on heating is called cubical expansion.
Increase in volume,

0V₂ = V₁ (1 + γ Δt)

where, V₁ and V₂ are initial and final volumes and γ is a coefficient of cubical expansion.

Coefficient of cubical expansion,

γ = \(\frac{\Delta V}{V \times \Delta t}\)

where V =real volume, ΔV = change in volume and Δt = change in temperature.

Dimension of α, β and γ are same [θ^-1] and units are K^-1 or (°C)^-1

Relation between coefficients of linear, superficial and cubical expansions.
β = 2a and γ = 3a
or
α : β: γ = 1 : 2 : 3

2. Expansion of Liquids
In liquids only expansion in volume takes place on heating.

(i) Apparent Expansion of Liquids:
When expansion of the container containing liquid, on heating is not taken into account, then observed expansion is called apparent expansion of liquids.

Coefficient of apparent expansion of a liquid

(γ_a) = \(\frac{\text { apparent(or observed) increase in volume }}{\text { original volume } \times \text { change in temperature }}\)

(ii) Real Expansion of Liquids:
When expansion of the container, containing liquid, on heating is also taken into account, then observed expansion is called real expansion of liquids.

Coefficient of real expansion of a liquid

(γ_r) = \(\frac{\text { real increase in volume }}{\text { original volume } \times \text { change in temperature }}\)

Both γ_r and γ_a are measured in °C^-1.

We can show that
γ_r = γ_a + γ_g

where, γ_r and γ_a are coefficient of real and apparent expansion of liquids and γ_g is coefficient of cubical expansion of the container (vessel).

Note:
Some substances contract with rising temperature because transverse vibration of atoms of substance dominate on the longitudinal vibration which is responsible for contraction.

Anamalous Expansion of Water
When temperature of water is increased from 0°C, then its volume decreases upto 4°C, becomes minimum at 4°C and then increases. This behaviour of water around 4°C is called anamalous expansion of water.

3. Thermal Expansion of Gases
There are two types of coefficient of expansion in gases

• Volume Coefficient
• Pressure Coefficient

(i) Volume Coefficient (γ_V):
At constant pressure, the change in volume per unit volume per degree Celsius is called volume coefficient.

γ_V = \(\frac{V_{2}-V_{1}}{V_{0}\left(t_{2}-t_{1}\right)}\)

where V₀, V₁ and V₂ are volumes of the gas at 0°C, t₁°C and t₂°C.

(ii) Pressure Coefficient (γ_p):
At constant volume, the change in pressure per unit pressure per degree Celsius is called pressure coefficient.

γ_p = \(\frac{p_{2}-p_{1}}{p_{0}\left(t_{2}-t_{1}\right)}\)

where p₀, p₁, and p₂ are pressure of the gas at 0°C, t₁°C and t₂°C.

Variation of Density with Temperature

Most substances expand when they are heated i.e. volume of a given mass of a substance increases on heating, so density decreases. Hence
ρ ∝\(\frac{1}{V}\),
ρ’ = ρ(1 + γΔT)^-1, as γ is small (1 + γΔT)^-1 ≈ 1 – γΔT
ρ’ ≈ ρ(1 – γΔ T)

Practical Applications of Thermal Expansion

1. When rails are laid down on the ground, space is left between the end of two rails.
2. The transmission cables are not tightly fixed to the poles.
3. The iron rim to be put on a cart wheel is always of slightly smaller diameter than that of wheel.
4. A glass stopper jammed in the neck of a glass bottle can be taken out by heating the neck of the bottle.

Thermometry and Calorimetry:
The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Heat Energy	Temperature and its Measurement
Thermometric Property	Thermometers
Thermal Expansion	Thermal Equilibrium
Triple Point of Water	Specific Heat Capacity
Thermal Capacity	Water Equivalent
Latent Heat	Joule’s Law
Calorimetry