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

## 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 .

## 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 Q1 is 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 10-3 mK

## Steffan's Law of Radiation

Q = σAT4 (for PBB)

Q = σeAT4

σ = 5.67 x 10-8 Wm-2K-4