# Thermal

Triple Point of Water

It is the state at which the three phases of water (Ice, Liquid Water and Water Vapours) co-exist in equilibrium. It occurs at a specific temperature of 273.16 K and specific pressure of 0.46 cm of Hg column.

Absolute Temperature

Kelvin Temperature Scale is called Absolute Scale.
Absolute Temperature = 0 K
Because below Zero Kelvin – No Temperature is possible.

This is why the SI unit of temperature is also Kelvin (K).

Thermal Expansion

Expansion of solid when they are heated is called Thermal Exapnsion.

It is of three types :

Linear Expansion –
It is the increase in the length of a metal rod on heating.

Coefficient of Linear Expansion (α)
α = ΔL/L ΔT
The coefficient of linear expansion of a material is defined as the increase in length per unit original length per degree rise in temperature.
The SI unit of α is K-1 ( Per Kelvin)

Superficial Expansion / Area Expansion –
It is the increase in the surface area of a metal sheet on heating.

Coefficient of Superficial Expansion ( β )
β = ΔA/A ΔT
The coefficient of superficial expansion of a material is defined as the increase in Area per unit original area per degree rise in temperature.
The SI unit of β is K-1 ( Per Kelvin)

Cubical Expansion / Volume Expansion –
It is the increase in the volume of the block on heating.

Coefficient of Cubical Expansion ( γ )
γ = ΔV/V ΔT
The coefficient of cubical expansion of a material is defined as the increase in volume per unit original volume per degree rise in temperature.
The SI unit of γ is K-1 ( Per Kelvin)

Coefficient of Thermal Conductivity (K)
K = Q.x/A(T1-T2)t
If A = 1
T1-T2 = 1
t = 1
x = 1
then Q = K

Hence, Coefficient of thermal conductivity of a material is defined as the quantity of heat that flows per unit time through a unit cube of the material when its opposite faces are kept at a temperature difference of one kelvin.

SI unit of K is JS-1m-1K-1

Methods of Transfer of Heat

Heat can be transferred from one place to another by three modes :

a) Conduction – In this method heat is transferred from particle to particle in the direction of fall of temperature without any actual motion of heated particles.
All solids are generally heated by conduction.
b) Convection –In this method heat is transferred from one place to another by the actual motion of heated particles.
Fluids are generally heated by the method of convection.
c) Radiation – In this method, the heat is transferred from the source to the receiver without any actual motion of source or receiver and also without heating the in-between medium.
For Example – The heat from the sun reaches to us through radiation.

Newton’s Law of Cooling

It states that the rate of loss of heat of a body is directly proportional to the temperature difference between the body and its surrounding, provided the temperature difference is small.

Mathematically,
Let T = Temperature of the body
T₀ = Temperature of the surrounding.

dQ/dt ∝ (T- T)

-dQ/dt = K (T- T)

Where K is a constant.
For Numerical Problems, The Formula for Newton’s law of Cooling Would be

dT/dt = -K (T- T)

Q. A body cools from 80° C to 60° C in 2 minutes. In how much time will it cool from 60° C to 40° C? The temperature of surrounding is 10° C.

Solution:

Case I
dT = 20 ° C
T (Average Temperature) =(T1+T2)/2 = 70° C
dt = 2 minutes
T = 10 ° C
Using Expression for Newton’s Law of Cooling

dT/dt = -K (T- T)
20/2 = -K (70-10)
10 = -60K ———-(1)

Case II
dT = 20 ° C
T (Average Temperature) =(T1+T2)/2 = 50° C
dt = ?
T₀ = 10 ° C
Using Expression for Newton’s Law of Cooling
dT/dt = -K (T- T₀)
20/2 = -K (50-10)
20/dt=-40K——-(2)

Dividing (1) by (2)
dt = 3 minutes