✤ Heat: It is the form of energy lay which we feel warmth

                      Unit → Joules                          ① Internal Energy             ② Kinetic Energy                    

                      CGS → Calorie

                          1cal ≅ 4.186J or 4.186x10^7 erg | cal-1

✤ Temperature: It is defined as the degree of hotness or coldness Temperature Scale:

                                          °C: Freesing Point → 0° g H₂O

                                            Boiling Point → 100°g H₂O

                                                        each part represent 1°c

                                             °F → C-0/100= F-32/180

                                                    

                             Note: -40°C is same for both f scale & C scale.

 Kelvin Scale: In this side freezing point 278 K & Boiling point 373K.

                        0°C = 273K

                    0°C = (t+273)K

❈ Absolute Temperature: It is the temp. in Kelvin at enrich volume of gas become zero. "No temp is possible below this temperature".

                  Absolute temperature → 273.16K

                            NOTE: Triple point of Water:

                                                It us point where three states greater.

                                                Coexist in equilibrium

                                                Ptr = 0.46cmg Hg

                                                Tsr = 273.16 K or 0.01°C

                                     Gay Lussa's Law: Ptr/Ttr = P/T

✤ Thermal Expansion : Expansion due to heat in a leady.

          (I) Linear Expansion : Increment in the length of a wire due to heat

                               By the experiment: Δl α l - ① from ⑪&② Δl α Δt

                                                                        Δl α Δt - ② Δl = αlΔt

                                               Here 'α' is called temperature coefficient

                                                                          α=Δl/ l XΔt

                                                                   Final length = l’ = l(1+αΔt)

        (ii) Areal Expansion: Due to increment is temperature size of a body increases. It is called areal Expansion. By the experiments

                                                                   Final Area→ A'= A (1+βΔt) β=ΔΑ/AΔT

        (iii) Volume Expansion : Increement in Volume of a solid cube is called volume expansion

                                                           :. V α VΔt

                                                ΔV= γVΔT Final Volume→ V'= V(1+γΔt)

                               Here γ=ΔV unit ᵒc⁻¹ Final density → p'= p(1-γΔt)

        Relation B/w α, β, γ

                      α:β:γ = 1:2:3

                           β=2α

                           γ=3α

        Proof :- Relation Hwx & B

                          let a square sheet of side l

                          We know, δl = k l δt

                               ΔΑ = ΒΑΔt

                          (l+Δl)² - l² = BAΔt

                           l² + Δl² + 2lΔt - l² = BAΔt

                           2lΔl = BAΔt

                           2l x Δt = Bl²Δt

                                 ß=2α,

                    Let a cube side lee a length l

                    We Know, Δv=α l Δt

                                    Δv= γ V Δt

                            (l+Δl)³- l³ = γ V Δt

                        l³ + Δl³ + 3l²Δl + 3lΔl² - l³ = γ V Δt

                                3l² Δl = γ V Δt

                                3l² (α l Δt) = γ V Δt

                            3 α l² δt = γ V Δt

                                        3α=γ

                                            γ = 3α

✤ Water Equivalent :- It is defined as the amount of water vehicle absorb same amount of heat as it absorbs by Given substance

           We know, H = WΔT

                   Let any substance of mass 'm' absorbs same energy

                           :. H = msΔT

                 wΔT = msΔT S-Specific heat Sl unit = kg

                          m- mass

✤ Heat Capacity :- It is defined as the amount of heat absorbed by a body.

          By the experiments

                      H α m ------ (1) In SL Arora level specific heat is

                      H α ΔΤ -----(2) determine by ‘c’ & Molar specific heat

                From (1) & (2) by ‘C’.

                         H α MΔT

                         H=SmΔT

                                       Hence s is called specific heat S – H/MΔT units

✤ Specific Heat: ⇒ It is defined as the amount of heat required by a body of 1kg to raise its temperature by 1° degree.

✤ Calorimetry: ⇒ It is a process by which we can measure the specific heat of a given substance by the help of Calorimeter.

                                ΔV

                        ⇒ It is used in many questions

✤ Principle: ⇒ It is based on the fact that loss of energy =  Gain in energy

                                  Let mass of water = m & temperature = t1

                                Let mass of a substance = M& temperature = t2

                        When substance (hot) is mixed with water & final temp be ‘t’.

                               ∴ Heat gained by the water = (m+w) (t-t1)

                                       Heat loss by the substance = MS.(t2-t1)

                        By the Principle,

                                 Heat Gain = heat loss

                                        (m+w) (t-t1) = MS(t2-t)

                Specific heat - (m+w)(t-t₁) / M (t₂-t)

✤ Latent Heat:- It is defined as the amount of heat required to change physical state without change physical temperate

                         Q = mL ⇒ Latent heat

                   L = Q / m units: Joules Kg⁻¹ or Calorie gm⁻¹

            Types:-

        ✤ 1 Calorie = 4.186 Joule

                  Joule's Mechanical equivalent of heat = W

Kinetic interpretation of temperature:-

        => The Temperature of a body is the measure of the average Kinetic energy

                          KE & Temperature

❈ Heat

          → It is a flowing energy which produces in us the sensation of hotness or Coldness

          → It is a Cause

          → It represent total KE

          → Flows from high tomborature.

❈ Temperature

          → Temperature is the degree of hotness or Coldness a body

          → It is an effect

          → It represents avg KE

          → Temperature decides the direction of heat flow

✤ Regelation: The phenomenon in which ice melts when pressure is increased & again freezes when pressure is removed (re-again, gelane- breeze)

❉ Question Tip:-

          When two scales of different nature is Given, length of one we will have to find then.

✤ FUSION:-

              It is the change from liquid to solid is called Fusion.

              A Plot temperature v/s time showing the changes in the star of ice on heating (net to scale)

                          EFFECT OF PRESSURE ON MELTING POINT BOILING POINT-

                                  Boiling point increases with increases

                                      In pressure i.e. B.P α P

                                  Melting point of those substance are expands on melting (Ex- Wax)

                                      increases worth increase in pressure

                                  Melting point of those substance contract (ice) decrease with increase in pressure.

                ✤ Anomalous expansion of Water: When water is at O C is heated, its volume decreases & therefor its density increases until it temperature                                         reaches 4°C. Above 4°C, the volume increases therefore the density decrease. Thus at 4°C water has maximum density.

✤ THERMAL CONDUCTIVITY :-

                It is the ability of a material (like metal) to conduct heat.            Rate of transfer of heat

                                                                            dQ/dt α -1 ----- (1)

                                                                        dQ/dt α (T1 - T2) ------ (2)

                                                                                 dQ/dt α 1/x ----(3)

                                                      from (1), (2) & (3)

                                                                            dQ/dt α A (T1 - T2)/x

                                                                               dQ/dt = K A (T1 - T2)/x Here, K is called coefficient of thermal conductivity

                  Now, K = (dQ/dt). x/A(T1-T2) when heat is transferred through a surface of 1m² & thickness of 1 unit by the difference in temperature 1°C is                     equal to the coefficient of thermal Conductivity.

                      Unit of k = J x sec-1 x m / m². °C

                                     = Jm-1sec-1 °C-1 or Wm-1K-1

                                    dim equation = ML2T-2 , L-1T-1K-1 = [MLT-8K-1]   

✤ MOLAR SPECIFIC HEAT :- It is defined as the amount of heat required to raise the temperature of 1gm mole of a substance by 1°C.

                                      C = ST or C = dQ/n ΔT

                                     n= no. of moles

     There are two types :-

                 (1) At constant Pressure: It is defined as the amount of heat required by 1 mole gas by 1°C increases at constant Pressure. It is denoted by Cp.

                 (2) At Constant Volumes It is defined as the amount by heat required of one mole gas to raise its temp by 1°C at Constant Volumes.

             Relation b/w Cp & Cv

                      ① Cp - Cv = R

                      ② Cp > Cv

                      ③ Cp/Cv = γ

✤ Newton's law of cooling -> It is states that rate of heat lost by a body is always proportional to the difference in temperature b/w body & surrounding -                         Provided that differences in temp is small or surrounding is constant.

                                                    -dQ2/dt (T-To) T = Temp. of heat body

                                                         -dQ/dT = K (T - To)

                                                             dQ / dt = -k(T - To)

                                    We know QkT

                                                            => dT/dt = -l (T-To)

                                                                => dt/T-TO

                                                              ∫dT/T-TO= -K ∫dt

                                                          log |T-To| = - Kt + C

                                                              T - To = -Kt

✤ Stefan's Boltzman Law: when a black body at temperature T is placed in an enclosure at temp. To, it radiates heat energy per unit area,

                                                                  E = σ(T⁴-T₀⁴)

✤ Stefan's law: → It states that heat lose by a perfectly black body per unit area per second is always proportional to the fourth power by the absolute                               temp. of the body.

                                                                        E ∝ T⁴

                                                                            E = γ T⁴

                                                        γ = 5.67 x 10⁻⁸ J sec⁻¹ m⁻² K⁻⁴

                                                        γ = 5.67 x 10⁻⁸ Wm⁻² K⁻⁴

                                                        γ = Stefan's constant

                                                        γ = 5.67 x 10⁻⁵ ergs cm⁻² K⁻⁴

       Energy radiated by a surface of emissivity ε, A in time t:

                     (i) E = εσT⁴ x A x t              (ii) E = εσ(T⁴ - T₀⁴) x A x t

✤ Question Tip :-

          Changes in temperature at a point distant 10cm from the hot end = Temperature gradient x distance = Product

                          Temperature gradient at this point + Product = Temperature

          If the thickness is increased then mass of ice to be frozen

                             m = A x thickness increased x density

      Average thickness = ( thickness increased + given thickness ) / 2

                                        Temperature gradient = ΔT / x

✤ Wien's displacement:

        It states that wavelength of the energy emitted by a perfectly black body is maximum. This wavelength is always inversely proportional to absolute         temperature of the body.

                λm = b/Temp here b is called Wien's constant

                       b = 2.9 x 10⁻³ mK

✤ Question's Tip:

            Fraction change of density. Po-Pt / Po = γ ΔT

        Short Questions:

             →   Clinical thermometer should not be sterilized by boiling because the range of clinical thermometer is usually from 95°F to 110°F & the

                   boiling point of water is 212°F.

             →  Triple point of water is the temperature at which three phases of water: ice, liquid & water vapour exist simultaneously. It is unique because it                   occurs at specific temperature 273.16k & a specific pressure of 0.46 cm Hg.

             →  The temperature of a body cannot be negative on Kelvin Scale this is because the absolute zero on the Kelvin scale is the min. possible

                   temperature.

             → tC = lt - l₀ / l₁₀₀ - l₀ × 100°C

             → The bodies at different temperatures T₁ & T₂, if brought in thermal contact do not settle at necessary temperature (T₁ + T₂)/2 because two                   bodies may have different masses different thermal capacities.

             → All solids do not expand on heating. For eg: Camphor.

             → The avg distance b/w the positions of equilibrium of the atoms of a solid increases with an increase in temperature which results in

                   thermal expansion of a solid.

             → Temperature coefficient always+ve. Temperature Coefficient is +ve for metals & -ve for semiconductors for insulators.

             → If no gap is left btw the iron rails, the rails may bend due to expansion in summer & the train may get derailed.

             → Pendulum clocks Generally run fast in winter & slow in summer because the time period ∝ length

                                        T = 2x√(l/g)

                                            T α √l

             → Iron rims are heated red hot before being put on the cart wheels.

                           When the iron ring is heated to become red hot it expands & slips on touch easily. when it is cooled it contracts & grips the wheel firmly

             → Specific heat is heat capacity per unit mass, molar heat is heat capacity per unit mole

             → Water is preferred to any other liquid in hot water bottles because due to specific heat it does not cool fast. Also for the Given mass of

                   water, the amount of heat contained is higher & it can provide more warmth as compared to any liquid

             → Water is used as an effective coolant in an automobile radiators because the specific heat of water is high when it runs over hot parts

                   of an engine or machinery it absorbs a large amount of heat.

             → An icebox is constructed with a double wall & the space. b/w the walls is filled with some non-conducting material to provide hard

                   insulation, so that loss of heat can be minimized.

             → We cannot easily boil water in a paper cup this because heat is easily conducted through the paper to water as such the temperature

                   attained is not sufficient for the paper to be charred.

             → Thes thin blankets are warmer than a single blanket of double the thickness because it the air enclosed b/w two blankets prevents the

                   transfer of heat from our body to outside

             → Water is heated from below, its density decreases & it rises up cooler liquid of the upper point takes its place & so convection currents and

                   set up & Water gets & catchup.

             → The total energy radiated by a body depends on its surface area. Thus when the animals feel very cold they use their bodies which in turn

                   helps to reduce the amount of heat.

             → All black coloured objects are considered black bodies is not always correct. A polished black surface is not a black body because it

                   reflects. In the same way dazzling white sun is a black body.

             → Blackbody radiation is white because A black body absorbs radiations of all wavelengths when heated to a suitable temp it emits

                   radiations.

✤ Reflectance: It is defined as the ratio of the amount of thermal energy reflected by a body is a certain time to the total amount of thermal energy falling                         upon the body in the same time                         :. Reflectance, r=R/Q

✤ Absorptance: It is defined as the ratio of the amount of thermal energy absorbed by a body in a certain time to the total amount of thermal energy                             incident upon the body in the same time

     :. Absorptance, a=A/Q

✤ Transmittance:   It is defined as the ratio of the amount of thermal energy transmitted by a body in certain time to the total amount of thermal radiation                                 on it in the same time.

                                                 :. Transmittance = t = T/Q

                                  r, a, t depend upon nature of the body & Wavelength of incident   radiation.

                                                          r + a + t = 1

 ❆ Special Cases:

                 (1) If t = 0, r + a = 1

                           Clearly, if r is more, a is less & Vice Versa That is Good reflectors are lead absorbers & bad reflectors are Good absorbers heat.

                 (2) If r=0 & t=0 not transmitted, then a = 1. a body which neither reflects nor transmits lead absorbs where of heat radiation incident on it is                         called a black body.

✤ Absorptive Power:

          The absorptive power of a body for a given wavelength λ is defined as the ratio of amount of heat energy absorbed in a certain time to the

          total heat energy incident on it in the same time within a unit wavelength range around the wavelength λ .

          Black body absorptive power is unity.

          Absorptive power is a dimensionless quantity.

✤ Emissive Power:

          The emissive power of a body at a given temperature T for a given wavelength λ is defined as the amount of radiant energy emitted per unit surface             area of the body within a unit wavelength range around the wavelength λ .

                          SI unit is Emissive Power = Js⁻¹ or Wm⁻².

✤ Emissivity:

          The emissivity of a body is defined as the ratio of the heat energy radiated per unit time per unit area by the given body to the amount of heat energy             radiated per unit time per unit area by a perfect black body of the same temperature.

                        E = e / E

                    E = emissivity

                    E = emissive power of a black body

                    e = emissive power of a given body

              It is a dimensionless quantity.

          Emissivity of a perfect black body is 1.

      A black body is one which is neither reflects nor transmits but absorbs whole heat of radiation incident on it. The radiations emitted by a black body       are called full black body radiations.

      Kirchoff's law of heat radiation states that at any given temperature the ratio of emissive power to absorptive power corresponding to a certain       wavelength (λ) is constant for all bodies & this constant & this constant is equal to emissive power of a perfect black leady at the same temperature &       at the same wavelength.

                    eλ/aλ = Eλ(Constant)

                 as eλ/Eλ = aλ, & eλ/Eλ = E

                        [ aλ = ε ]

      Hence, a good absorber is a good emitter, since a good absorber is a poor reflector, so the ability of a body to emit radiation is related oppositely to its         ability to reflect Thus, a good emitter is a lead reflector.