Thermodynamics & Radiation

This Chapter is related to Thermal Physics

For Chemistry Section, go to Chemical Thermodynamics

Heat
The energy that is transferred from one body to another, without any mechanical work involved , is called heat. Heat is meaningful as long as there is transfer of energy. Unit : Joule, Calorie

1 Calorie = 4.18 Joule

Scales of Temperature
Celsius

Fahrenheit

Kelvin

Thermal Expansion
(All temperatures in oC)

Calibration of Thermometers
1) Mercury Thermometer : 

Mercury thermometer works on the principle of linear expansion. A certain change in temperature brings a certain change in length of mercury column. This change can be easily calculated by the formula of linear expansion, if we know the coefficient of linear expansion of mercury and its original length at 0o C.

2) Electric Thermometer :

The resistance of the thermometer coil changes with changes in the temperature. This change is detected by an external circuit, responsible for displaying the temperature.

Calorimetry
Calorimetry is the measurement of heat i.e. energy transferred between two bodies.

The principle of Calorimetry states that the total heat energy given by the hot objects equals the total hat energy absorbed by cold body.

Specific Heat Capacity
c = Q / m∆θ      cv= Q / m∆θ       cp= Q / m∆θ

cp - cv= R

cm= Q / n∆θ  Molar Specific Heat Capacity

γ = cp/cv

Latent Heat
The heat energy required to change the state of matter is called as Latent hat of Fusion.

Specific Latent Heat = Q / m

Mechanical Equivalent of Heat
W = J H

where Work W produces same temperature change as Heat H and J is a constatn called as mechanical equivalent of Heat.

Thermal Conductivity
Thermal Conductivity

Q = KA[∆θ/x]t, where K is the thermal conductivity.

Thermal Resistance

Q/t∆θ = KA/x [from above equation]

t∆θ / Q = x/ KA

t∆θ / Q = R where R is the Thermal Resistance (Reciprocal of KA/x)

Series Connection :

R = R1 + R2+ R3+ .... + Rn

Parallel Combination :

1/R = 1/R1 + 1/R2 + 1/Rn + .... + 1/Rn

Convection and Radiation
Convection is the process of transfer of heat by the actual mobility of particles.

Radiation is the emission of electromagnetic waves of frequency υ and energy hυ or hc/λ. The speed of an radiation is equal to the speed of light.

Newton's Law of Cooling
Rate of Cooling = K (θ - θo)

Newton's Law of Cooling is applicable only for temperature difference of less than 10o C

Prevost Theory of Exchange

 * 1) A body having temperature equal to it's surroundings, radiates energy at the same rate as it absorbs energy
 * 2) A hot body placed in cool surroundings, radiates energy faster than what it absorbs.
 * 3) A cool body placed in hot surroundings, absorbs energy faster than what it radiates.

Zeroth Law of Thermodynamics
Zeroth Law of Thermodynamics states that if two bodies P and Q are in thermodynamic equilibrium, and also P and R are in thermodynamic equilibrium then , Q and R are also in Thermodynamic Equilibrium.

Laws of Thermodynamics
1) ∆U = q + W

2) Mechanical Work can be converted completely into heat energy, but heat cannot be completely converted into mechanical work . i.e. heat and mechanical energy are not equivalent.

3) Th entropy of a perfectly ordered crystalline substance at absolute zero temperature is zero.

First Law of Thermodynamics and it's Applications
(For ideal gases only)

Heat Engines
An heat engine works in cyclic process. It takes heat from bodies at higher temperature, converts part of it into mechanical work and and remaining to a body at lower temperature.

Efficiency of Heat Engine (η) = W / Q1; where Q1 is the heat input and Q2 is the heat output.

W = Q1 - Q2

η = 1 - Q2 / Q1

T1/T2 = Q1/Q2

Refrigerators
A refrigerator is the reverse of a heat engine. The refrigerator extracts heat (Q2) from cold reservoir at temperature T2, external work W is done on it and Q1is released to hot reservoir at temperature T2.

α = Q2 / W

W = Q1 - Q2

α = Q2 / Q1 - Q2

Absorption and Reflection
Q = Qa + Qr + Qt

Coefficient of absorption (a)

a = Qa / Q

Coefficient of reflection (r)

r = Qr / Q

Coefficient of transmission (t)

t = Qt / Q

1 = a + r + t

Athermanous Substances

The substances which do not transmit any incident heat radiations are called as athermanous substances.

Diathermanous Substances

The substances which are transparent to heat radiations are called as diathermanous substances.

Perfectly Black Body
Perfectly black body is a body which completely absorbs all the radiant energy incident on it.

Emissive Power and Absorptive Power
Absorptive Power = a = Qa / Q

Emissive Power = E = Q / At

Emissivity = e = E(body) / E(PBB)

Kirchoff's Law of Radiation
E(body) / a = E(PBB)

a = e

Wien's Displacement Law
λm = b/T

b = 2.898 x 10-3mK

Steffan's Law of Radiation
Q = σAT4(for PBB)

Q = σeAT4

σ = 5.67 x 10-8 Wm-2K-4