Notes on thermal properties of matter

 📖Notes on Thermal Properties of Matter

Expansion in two dimensions (Superficial expansion):-

When the thermal expansion of a body is confined to a plane, it is to be two dimensional expansion or superficial expansion.

Coefficient of superficial expansion (β):- It is defined as the change in area of the surface per unit area at 0ºC, per degree centigrade rise of temperature.

β = St-S0/S0t

Expansion in three dimensions (Cubical expansion/volume expansion):- When thermal expansion of the body takes place in space, it is said to be three dimensional expansion or cubical expansion.

Coefficient of cubical expansion (γ):- Coefficient of cubical expansion is defined as the change in volume per unit volume, at 0ºC, per degree celsius rise of temperature .

γ = Vt-V0/V0t

Relation between expansion coefficients:-

(a) Relation between α and β:    β = 2α

(b) Relation between α and γ:    γ= 3α

(c) Relation between β and γ:    γ = 3/2 β

(d) α : β : γ = 1:2:3

Thermal expansion of liquids:-

(a) Co-efficient of apparent expansion (γa):- The coefficient of apparent expansion of a liquid is defined as the apparent  (or observed) increase in volume, per unit volume of the liquid at 0ºC per degree celcius rise of temperature.

γa = apparent increase in volume/(original volume at 0ºC) × (rise of temperature)

(b) Co-efficient of real expansion (γr):- The coefficient of real expansion of a liquid is defined as the real increase in volume, per unit volume of the liquid at 0ºC per degree centigrade rise of temperature.

 γa= real increase in volume/(original volume at 0ºC) × (rise of temperature)

Work and Heat:-

Whenever heat is conserved into work or work into heat, the quantity of energy disappearing in one form is equivalent to the quantity of energy appearing in the order.

W∝H  or W = JH

Joule’s mechanical equivalent of heat is defined as the amount of work required to produce a unit quantity of heat.

J = W/H

Value of J:- J = 4.2×107 erg cal-1 = 4.2 J cal-1

Specific heat capacity or specific heat (c):-

Specific heat capacity of a material is defined as the amount of heat required to raise the temperature of a unit mass of material through 1ºC.

c = Q/mΔT

Unit:- kcal kg-1K-1 or J kg-1K-1

Dimension:- M0L2T-2K-1

Molar specific heat capacity(C):-

Molar specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of one gram molecule of the substance through one degree centigrade.

(a) C = Mc  (Here M is the molecular weight of the substance)

(b) C = 1/n (dQ/dT)

Heat Capacity or Thermal Capacity:-

It is defined as the amount of heat required to raise the temperature of body through 1ºC.

Q = mcΔT

If ΔT = 1ºC, Q = heat capacity = mc

Unit:- kcal K-1 or JK-1

Water Equivalent:-

Water equivalent of a body is defined as the mass of water which gets heated through certain range of temperature by the amount of heat required to raise the temperature of body through same range of temperature.

w = mc

Water equivalent of a body is equal to the product of its mass and its specific heat.

Latent Heat:- When the state of matter changes, the heat absorbed or evolved is given by: Q = mL. Here L is called the latent heat.

(a)Specific latent heat of fusion (Lf):-

Specific latent heat of fusion of a substance is defined as the amount of heat required to convert 1 gram of substance from solid to liquid state, at the melting point, without any change of temperature.

(b) Specific latent heat of vaporization (Lv):-

Specific latent heat of vaporization of a substance is defined as the amount of heat required to convert 1 gram of liquid into its vapours at its boiling point without any rise of temperature.

Dimensional formula:- M0L2T-2

Unit:- kg cal kg-1  or J kg-1

Triple point of water = 273.16 K

Absolute zero = 0 K = -273.15ºC

For a gas thermometer, T = (273.15) P/Ptriple (Kelvin)

For a resistance thermometer, Re = R0[1+αθ]