# Conduction of Heat – study notes

Conduction is a mode of transmission of heat where heat flows from the hot end to the cold end and particles of the medium simply oscillate but do not leave their place.

**Conduction of Heat has the following characteristics:**

- Medium is necessary for conduction.
- It is a slow process.
- The path of heat flow may be zig-zag.
- Conduction takes place in solids.
- The temperature of the medium increases through which heat flows.
- heat flows from the hot end to the cold end and
- particles of the medium simply oscillate but do not leave their place.

## Conduction of Heat and related Terms

### Variable and steady state

If the temperature of every cross-section of the rod goes on increasing, then the rod is said to exist in a **variable state**.

If the temperature of every cross-section of the rod remains constant and no part of the rod absorbs heat then the state of the rod is called **steady state**.

### Isothermal surface

Any surface having its all points at the same temperature is called an isothermal surface.

### Temperature Gradient

The rate of change of temperature with the distance between two isothermal surfaces is called **temperature gradient**.

Temperature gradient = [( θ – Δθ) – θ ] / Δx = – Δθ / Δx

*The negative sign shows that temperature θ decreases as the distance x increases in the direction of heat flow.*

### Coefficient of thermal conductivity – formula

If L is the length of the rod, A the area of cross-section, and θ_{1} and θ_{2} are the temperatures of its two faces, then the amount of heat flowing from one face to the other face in time t is given by Q, where:

Q = KA ( θ_{2} – θ_{1} )t/L *Where K is the coefficient of thermal conductivity of the material of the rod.* K is also called thermal conductivity.

Rate of flow of heat or Heat Current = H = Q/t

=> H = KA ( θ_{2} – θ_{1} )/L

The greater the value of K for a material, the more rapidly will it conduct heat.

## K the coefficient of thermal conductivity – features

(i) Units = Js^{–1}m^{–1}k^{–1} or Wm^{–1}k^{–1} (S.I.)

CGS unit = cal s^{–1} cm^{–1} ºC^{–1}

(ii) Dimension : [MLT^{–3}θ^{–1}]

(iii) The magnitude of K depends only on the nature of the material.

(iv) For perfect conductors, K = ∞ and for perfect insulators, K = 0

(v) The thermal conductivity of pure metals decreases with the rise in temperature but for alloys, the thermal conductivity increases with the increase in temperature.

## Thermal conductivities (K) of some material

Material | Thermal conductivity (K) |
---|---|

Silver | 406 |

Copper | 385 |

Aluminium | 205 |

Brass | 109 |

Steel | 50.2 |

Lead | 34.7 |

Mercury | 8.3 |

Glass | 0.8 |

Ice | 1.6 |

Wood | 0.12 |

Water | 0.8 |

Air | 0.024 |

Hydrogen | 0.14 |