### The expansion due to an increase in the temperature is known as thermal expansion.

Heat is a form of energy that is transferred between a system and its surrounding as a result of temperature difference. The expansion due to an increase in the temperature is known as thermal expansion. There are three types of thermal expansion, namely Linear, Superficial, and Volume expansion.

When there is any change in the length of a body due to heating then the expansion is called longitudinal or linear expansion.

Coefficient of Expansion: Δ1 = Change in length and Δt = Change in Temperature

α = limΔt → 0 1l0 ΔlΔt and Δl = l0 α Δtmathbf{alpha ;=;lim_{Delta t; rightarrow ;0};;frac{1}{l_{0}};;frac{Delta l}{Delta t};;and;;Delta l;=;l_{0};alpha ;Delta t} α = lim Δ t → 0 l 0 1 Δ t Δ l a n d Δ l = l 0 α Δ t

When there is any change in the area of a body due to heating then the expansion is called axial or superficial expansion.

Coefficient of Expansion: ΔA = Change in Area and Δt = Change in Temperature

β = limΔt → 0 1A0 ΔAΔt and ΔA = A0 β Δtmathbf{beta ;=;lim_{Delta t; rightarrow ;0};;frac{1}{A_{0}};;frac{Delta A}{Delta t};;and;;Delta A;=;A_{0};beta ;Delta t} β = lim Δ t → 0 A 0 1 Δ t Δ A a n d Δ A = A 0 β Δ t

When there is any change in the volume of a body due to heating then the expansion is called volumetric or cubic expansion.

Coefficient of Expansion: ΔV = Change in volume and Δt = Change in Temperature

γ = limΔt → 0 1V0 ΔVΔt and ΔV = V0 γ Δtmathbf{gamma ;=;lim_{Delta t; rightarrow ;0};;frac{1}{V_{0}};;frac{Delta V}{Delta t};;and;;Delta V;=;V_{0};gamma;Delta t} γ = lim Δ t → 0 V 0 1 Δ t Δ V a n d Δ V = V 0 γ Δ t

If α 1, α 2, and α 3 are coefficient of linear expansion in X, Y and Z directions, then,

α = α 1 = α 2 = α 3, β = 2α γ = 3α

β = α 1 + α 2 and γ = α 1 + α 2 + α 3

If temperature of a rod of length l0 clamped between two fixed walls separated by same distance l0 is changed by amount Δt then,

Stress = F / A and Strain = Δ1 / 1 o

Therefore, Young’s Modulus = FAΔll0 = F l0A Δl = FA α Δtmathbf{frac{frac{F}{A}}{frac{Delta l}{l_{0}}};=;frac{F;l_{0}}{A;Delta l};=;frac{F}{A;alpha ;Delta t}} l 0 Δ l A F = A Δ l F l 0 = A α Δ t F

i.e. F = Y A α Δtmathbf{F;=;Y;A;alpha ;Delta t} F = Y A α Δ t

A. If α varies with distance [ α = ax + b]

Total thermal expansion = ∫01 (ax + b) dx Δtmathbf{int_{0}^{1};;left ( ax;+;b right );dx;Delta t} ∫ 0 1 ( a x + b ) d x Δ t

B. If α varies with temperature [ α = f (T)]

Δl = ∫T1T2 α l0 dTmathbf{Delta l;=;int_{T_{1}}^{T_{2}};alpha ;l_{0};dT} Δ l = ∫ T 1 T 2 α l 0 d T

Variation in Density: Density decreases with an increase of temperature because of the increase in volume and vice-versa i.e.

Density d = d01 + γ Δtmathbf{frac{d_{0}}{1;+;gamma ;Delta t}} 1 + γ Δ t d 0

Special Case: The Density water is maximum at 4 °C. Its density increases from 0 °C to 4 °C (g is positive). From 4 °C to higher temperatures g is positive.

While conduction is the transfer of heat energy by direct contact, convection is the movement of heat by actual motion of matter; radiation is the transfer of energy with the help of electromagnetic waves.

dQdT = K A dTdxmathbf{frac{dQ}{dT};=;K;A;frac{dT}{dx}} d T d Q = K A d x d T

Where, dT / dX = Temperature Gradient

It states that the net radiant heat energy emitted from an object is proportional to the 4th power of its absolute temperature.

E = σ A T4 J sec−1 m−2mathbf{E;=;sigma ;A;T^{4}};;J; sec^{-1} ;m^{-2} E = σ A T 4 J s e c − 1 m − 2

dQdT = σ A T4 wattmathbf{frac{dQ}{dT};=;sigma ;A;T^{4};;watt} d T d Q = σ A T 4 w a t t

If Ts is the surrounding temperature: [Black Body]

dQdT = σ A (T4 − Ts4)mathbf{frac{dQ}{dT};=;sigma ;A;(T^{4};-;T_{s}^{4})} d T d Q = σ A ( T 4 − T s 4 )

Emissive Power or Emissivity e = Heat from given body / Heat from a black body

It states that the rate of change of the temperature (T) of an object is proportional to the difference between its own temperature and the temperature of its surroundings.

T(t) = T s + (T o – T s ) e – k t

T o = Initial temperature of the body

T (t) = Temperature of the body at time t

At any temperature T greater than 0 Kelvin the body emits energy radiations of all wavelengths. According to the Wien’s displacement law, if the wavelength (λ) corresponding to the maximum energy is λ max then,

It is the measurement of changes in the state variables of an object for the purpose of deriving the transfer of heat associated with changes in its state either due to phase transitions, physical changes, or chemical reactions, under specified constraints. A calorimeter is a device using which Calorimetry is performed.

The amount of heat required to raise the temperature of 1 gram of water from 14.5° C to 15.5°C at Standard Temperature and Pressure (STP) is 1 calorie.

Q = m ∫T1T2 C dt = m C ΔTmathbf{Q;=;m;int_{T_{1}}^{T_{2}};;C;dt;=;m;C;Delta T} Q = m ∫ T 1 T 2 C d t = m C Δ T

L = latent heat of substance in Cal gm -1 0 C -1 or in Kcal kg -1 0 C -1

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Heat is transferred between objects by direct contact

Energy transition (heat transfer) occurs within the fluid

Heat is the transmission is done without any physical contact between objects

How heat travels between objects in direct contact

How heat flows through empty spaces

Occurs in solids through molecular collisions.

Occurs in fluids by the actual flow of matter.

Occurs at a distance and does not heat the intervening substance.

Occurs from all objects, at a temperature greater than 0 Kelvin