Thermal and Electrical

Conductivity of Metals

Objectives

• Determine the heat capacity of the calorimeter and measure the calefaction of water at 0°C due to action of ambient temperature.

• Determine thermal conductivity of metal rod.• Determine the electrical conductivity of metal rod by recording current

voltage characteristic line.• Verify the Wiedmann-Franz law.

Thermal Conductivity (Experimental set-up)

Thermal Conductivity

• Fourier’s Law : The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.

where λ is thermal conductivity which is the property of the material to conduct heat.

𝑑𝑄𝑑𝑡 =− λ A 𝜕𝑇𝜕 𝑥

Thermal Conductivity

The temperature distribution in a body is generally a functionof location and time and is given by following heat equation.

Where , is density

c is specific heat capacity

At steady state Substituting in above equation we get

𝜕𝑇𝜕𝑡 =

λ𝜌 ∙𝑐 ∙

𝜕2𝑇𝜕𝑥2

Q 𝑇 1 𝑇 2

LBoundary values

The Heat Capacity of the Calorimeter

Heat Capacity : The heat capacity of a substance is the amount of heat required to change its temperature by one degree.

Heat lost by hot water =

Heat gained by calorimeter =

Heat gained by calorimeter = Heat lost by water

Effect of heat from the surroundingsThe addition of heat from the surroundings is calculated fromthe temperature increase (T) of the cold water in the calorimeter.

where is temperature of water at t=0

dQ/dt for the ambient heat can be calculated from the slopeof the graph for calefaction of water.

In order to calculate the heat energy transported by the metal rod, this ambient heat fraction must be subtracted. Heat of surroundings over time.

Time (min)

Results

Time (min)

Time (min)

T as function of time for aluminium Q as a function of time for aluminium

Thermal conductivity ( ) = 140.7 Literature value of = 254.0

𝑑𝑄𝑑𝑡 =− λ A 𝜕𝑇𝜕 𝑥

Electrical Conductivity (experimental set-up)

Electrical Conductivity

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Electrical conductivity

Observed value of 5.76Literature value of 3.27

Wiedmann-Franz law:

Wiedmann-Franz law states that the ratio of thermal conductivity to the electrical conductivity is directly proportional to the absolute temperature. LT

where L is Lorenz Number

λ is Thermal conductivity is Electrical conductivity

Observed value of Lorenz number L = 0.8Literature value of Lorenz number L = 2

Proposal

• It is very difficult to achieve steady state since temperature of hot and cold reservoirs changes due to surrounding.

• We can use ice gauze pouch and keep it in lower calorimeter, so that its temperature remains at .

• Maintain the temperature of upper calorimeter constant using immersion heater.

Thank You

Sangram KadamIISER Bhopal13066