Physics Prana

Tag: Heat Transfer

Thermal Conductivity, Gas Laws & Specific Heat Explained with Formulas and Examples

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“Thermal Conductivity, Gas Laws & Specific Heat — Complete Guide for Students”

 1.Introduction:

    Heat plays an important role in our daily life and in every branch of science. Understanding how heat flows through materials, how gases behave under different conditions, and how substances absorb heat is essential in physics and engineering.

In this article, we will study:

  • Thermal Conductivity
  • Temperature Gradient
  • Gas Laws
  • Ideal Gas Equation
  • Heat Capacity and Specific Heat
  • Specific Heats of Gases

 2.Thermal Conductivity:

   When one end of a metal rod is heated and the other end is cooled, heat flows continuously from the hot end to the cold end through the process of conduction.

Consider a metal rod:

  • One end is kept in a steam bath (hot end).
  • The other end is kept in an ice bath (cold end).

   Initially, the temperature of every part of the rod increases. After some time, the temperature at each point becomes constant. This condition is known as the steady state.

At steady state:

  • Heat entering from the hot end equals heat leaving from the cold end.
  • Temperature decreases gradually from the hot end to the cold end.

Let:

  • Temperature at point M = θ₁
  • Temperature at point N = θ₂
  • Distance between M and N = d

 2.1. Steady State:

  “Steady state is the condition in which the temperature of each point of a conductor remains constant with time, although heat continues to flow through it.”

 2.2.Temperature Gradient:

   “The decrease in temperature per unit distance along the direction of heat flow is called the temperature gradient.”

Temperature gradient = (θ1 – θ2 ) / d 

Where:

  • θ₁ = temperature at hot point
  • θ₂ = temperature at cold point
  • d = distance between the two points

 2.3. SI Unit:

kelvin per meter (K/m)

 2.4.Law of Thermal Conductivity:

The amount of heat flowing through a conductor at steady state is:

  1. Directly proportional to the cross-sectional area (A)
  2. Directly proportional to the temperature gradient
  3. Directly proportional to the time of flow (t)

Therefore,      Q α A;       Q α (θ1 – θ2 ) / d ;          Q α t

         Q α A.t. (θ1 – θ2) / d 

         Q = k .A .t. (θ1 – θ2) / d    

Where:

  • Q = amount of heat transferred
  • A = cross-sectional area
  • t = time
  • d = distance between points
  • k = coefficient of thermal conductivity

 2.5.Coefficient of Thermal Conductivity:

The coefficient of thermal conductivity is defined as:

   “The amount of heat flowing per second through a material of unit cross-sectional area when there is a unit temperature gradient across it.”

 2.6.Units of Thermal Conductivity:

System

 Unit

SI Unit

 W/m·K
CGS Unit

cal/cm·s·°C
MKS Unit

kcal/m·s·°C

 3. Gas Laws:

   The behavior of gases is described using four physical quantities:

  1. Mass
  2. Volume
  3. Pressure
  4. Temperature

 Gas laws study the relationship between pressure, volume, and temperature when one quantity remains constant.

The three important gas laws are:

  1. Boyle’s Law
  2. Charles’s Law
  3. Gay-Lussac’s Law

 3.1. Boyle’s Law:

   PV=constant

  In 1662, Robert Boyle discovered that:

 “At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume”.

Thus,   P α 1 / V;   or  PV = constant at constant temperature.

    This indicates that at constant temperature, product of pressure and volume of a fixed mass of gas is constant.

     If a fixed mass of gas at constant temperature T occupying volume V1 at pressure P1 undergoes expansion, so that volume changes to V2 and pressure to P2, then according to Boyle’s law:

 

P1 . V1 = P2 . V2 = Constant.

Conclusion:

  • If pressure increases, volume decreases.
  • If pressure decreases, volume increases.

 3.2. Charles’s Law:

  V/T=constant

    Jacques Charles discovered that:

   “At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.”

Thus, V α T ; or  V / T  = constant at constant pressure.

    This indicates that at constant pressure, the ratio of volume of a fixed mass of gas to absolute temperature of gas is constant.

    If a fixed mass of gas at constant pressure P occupying volume V1 at absolute temperature T1 undergoes expansion, so that volume changes to V2 at absolute temperature T2, then according to Charles’s law :

 V1 / T1  = V2 / T2 = constant.

Important Relation:

For each degree change in temperature, the volume of sample of a gas changes by the fraction of 1/273.5 of its volume at 0 oC.

So   Vt  = V0 ( 1 + t/ 273 ).

  3.3. Gay-Lussac’s Law:

 P/T=constant

    Gay-Lussac’s law states:

   “At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature”.

    This indicates that at constant volume, the ratio of pressure of a fixed mass of gas to absolute temperature of gas is constant.

      If a fixed mass of gas at constant volume V, pressure P1 at absolute temperature T1 undergoes changes pressure to P2 at absolute temperature T2, then according to Gay-Lussac’s law :

 P1 / T1  = P2 / T2 = constant.

       For each degree change in temperature, the pressure of sample of a gas changes by the fraction of 1/273.5 of its pressure at 0 oC.

So   Pt  = P0 ( 1 + t/ 273 ).

 3.4. Ideal Gas Equation:

It is seen from gas laws for 1 mole of gas:

According to Boyle’s law  P α 1 /V,

According to Gay-Lussac’s law  P α T,

Hence, combining these, we get,  P α T / V,

Or   P V / T = Constant = R  or P V = R T

Where R is Universal gas constant = 8314.9 J / kg. mol. 0K .

For n moles of gas  P V = n R T .

The gas which obeys this equation P V = n R T is called Ideal or Perfect gas.

Where:

  • P = pressure
  • V = volume
  • n = number of moles
  • R = universal gas constant
  • T = absolute temperature

  3.5. Universal Gas Constant:

R = 8.314 J/mol·K
  “   A gas obeying this equation is called an ideal gas.”

 4. Heat Capacity:

Different substances require different amounts of heat to raise their temperatures.

Heat capacity is defined as:

   “The amount of heat required to raise the temperature of a whole body by 1°C.”

 4.1. Specific Heat Capacity:

  “Specific heat capacity is the amount of heat required to raise the temperature of unit mass of a substance by 1°C.”

C = Q / m ∆t

Where:

  • Q = heat supplied
  • m = mass of substance
  • Δt = rise in temperature
  • C = specific heat capacity

 4.2. Why Specific Heat is an Intensive Property:

Specific heat is an intensive property because:

  • It is defined per unit mass.
  • It does not depend on quantity of matter.
  • It depends only on the nature of the material.

  4.3. Units:

System Unit
SI Unit J/kg·K
CGS Unit cal/g·°C
MKS Unit kcal/kg·°C

  4.4. Specific Heat of Gases:

When gases are heated:

  • Their volume may increase.
  • Their pressure may increase.

Therefore, gases have two specific heats:

  1. Specific heat at constant pressure (Cp)
  2. Specific heat at constant volume (Cv)

 4.4.1. Specific Heat at Constant Pressure (Cp):

  “Specific heat at constant pressure is the amount of heat required to raise the temperature of 1 kg of gas by 1°C while keeping pressure constant.”

      Cp = Q / m ∆t

 4.4.2. Specific Heat at Constant Volume (Cv):

 “ Specific heat at constant volume is the amount of heat required to raise the temperature of 1 kg of gas by 1°C while keeping volume constant.”

      Cv = Q / m ∆t

4.4.2. Relation between Cp and Cv :

According to Mayer’s relation:

Cp – Cv = R / J

Where:

  • R = universal gas constant
  • J = Joule’s constant

 4.4.3. Ratio of Specific Heats:

The ratio of specific heats is represented by γ (gamma).

Cp / Cv = γ = 1.4

 5. Conclusion:

Thermal conductivity explains how heat flows through materials, while gas laws describe the behavior of gases under different conditions of pressure, volume, and temperature. Specific heat capacity helps us understand how substances absorb heat energy.

These concepts form the foundation of thermodynamics, heat transfer, and engineering physics.

 

Conduction, Convection and Radiation – Modes of Heat Transfer Explained with Examples

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Modes of Heat Transfer: Conduction, Convection and Radiation

1. Introduction:

     Nature always tries to maintain thermal balance. Whenever there is a temperature difference between two objects or regions, heat energy naturally flows from the hotter body to the colder body until thermal equilibrium is reached.

  Heat can transfer from one place to another by three fundamental modes:

1.Conduction

2.Convection

3.Radiation

    Each mode of heat transfer works differently depending on the material medium and motion of particles.

Heat transfer

2. Modes of Heat Transfer:

2.1. Conduction:

2.1.1.Definition:

      “Conduction is the process of transfer of heat from a region of higher temperature to a region of lower temperature through a material medium without actual movement of its particles.”

   During conduction, particles vibrate about their mean positions and transfer heat energy from one particle to another.

2.1.2.How Conduction Occurs?

  When one end of a metal rod is heated:

  • Particles near the hot end gain energy and vibrate faster.
  • These particles transfer energy to neighboring particles.
  • Heat gradually moves toward the colder end.

Conduction mainly occurs in solids, especially metals.

2.1.3.Important Characteristics of Conduction:

  • Requires a material medium
  • Most effective in solids
  • Does not occur in vacuum
  • No actual movement of particles
  • Comparatively slow process

2.1.4.Good Conductors of Heat:

    Materials that allow heat to pass through them easily are called good conductors.

Examples:

  • Copper
  • Aluminum
  • Iron
  • Silver

Therefore, cooking utensils, boilers, and calorimeters are usually made of metals.

2.1.5.Bad Conductors (Insulators):

    Materials that do not allow heat to pass easily are called bad conductors or insulators.

Examples:

  • Wood
  • Plastic
  • Wool
  • Rubber
  • Air

2.1.6.Applications of Conduction:

A. Pressure cooker handles are made of wood or plastic to prevent burns.

B. Ice is packed in sawdust because sawdust is a poor conductor of heat.

C. Woolen clothes and blankets reduce heat loss from the body during winter.

D. Calorimeters are insulated with cotton and placed in wooden boxes to minimize heat loss.

2.2. Convection:

2.2.1.Definition:

    “Convection is the process of transfer of heat in liquids and gases through the actual movement of particles from one place to another.”

The circulation of fluid caused by temperature differences is called convection current.

2.2.2.How Convection Occurs?

  When a liquid or gas is heated:

  • The heated particles expand and become lighter.
  • They rise upward.
  • Cooler and denser particles move downward.
  • This continuous circulation transfers heat.

2.2.3.Characteristics of Convection:

  • Occurs only in fluids (liquids and gases)
  • Requires actual movement of particles
  • Cannot occur in solids
  • Faster than conduction

2.2.4.Applications of Convection:

2.2.4.1. Chimneys in Factories:

       Factories and thermal power plants use tall chimneys because hot smoke and gases rise upward due to convection currents. Fresh cool air enters from below.

2.2.4.2. Ventilation in Auditoriums and Cinema Halls:

  Exhaust fans are installed near ceilings because warm air rises upward. Fresh cool air enters through doors and windows.

2.2.4.3. Formation of Winds:

      Air over hotter regions becomes warm and rises upward. Cooler air from surrounding regions moves in to occupy the space, creating winds.

2.2.4.4. Land and Sea Breezes:

Sea Breeze (Daytime):

Sea breeze

During the day:

  • Land heats faster than sea water.
  • Air above land becomes hot and rises.
  • Cooler air from the sea moves toward land.

This produces a sea breeze.

Land Breeze (Nighttime):

Land breeze

During the night:

  • Land cools faster than sea water.
  • Air above the sea remains warmer and rises.
  • Cooler air from land moves toward the sea.

This produces a land breeze.

2.2.4.5. Monsoon Winds:

 Monsoon winds are large-scale convection currents produced due to unequal heating of land and sea.

2.3. Radiation:

2.3.1.Definition:

   “Radiation is the transfer of heat energy in the form of electromagnetic waves without requiring any material medium.”

   Electromagnetic waves travel with the speed of light (C = 3 x108m/s).

   Therefore, radiation is the fastest mode of heat transfer.

2.3.2.Characteristics of Radiation:

  • Does not require a material medium
  • Can occur through vacuum
  • Travels in straight lines
  • Fastest mode of heat transfer
  • Heat from the Sun reaches Earth through radiation

2.3.3.Examples of Radiation:

  • Heat from the Sun reaching Earth
  • Feeling warmth near a fire
  • Heat emitted from electric heaters
  • Infrared radiation from hot objects

2.4.At a Glance: Comparison Table:

Feature Conduction Convection Radiation
Medium Solid required Fluid (Liquid/Gas) No medium needed
Particle Motion Vibration only Actual migration None
Speed Slowest Moderate Fastest
Example Metal spoon heating Boiling water Heat from Sun

 

3. Conclusion:

   Heat transfer is an important concept in physics and daily life. The three modes of heat transfer—conduction, convection, and radiation—operate through different mechanisms.

  • Conduction transfers heat through particle vibration.
  • Convection transfers heat through movement of fluids.
  • Radiation transfers heat through electromagnetic waves without any medium.

    Understanding these processes helps explain many natural phenomena and technological applications such as cooking, ventilation, weather systems, insulation, and solar heating.

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