THERMAL CONDUCTIVITY OF METAL ROD

TITLE: THERMAL CONDUCTIVITY OF METAL ROD

Objectives:

·       To determine the coefficient of thermal conductivity of metal rod.

Theory:

Thermal conductivity is a fundamental property of materials that describes their ability to conduct heat. Conduction is a process of heat transfer through solids. When a temperature gradient exists in a body, experiment has shown that there is a transfer of heat from the high temperature region. The heat transfer rate per unit area is proportional to the temperature gradient given by:

Where,

Q= heat transfer rate in watts

A = area of heat transfer in m²  

𝑑𝑇/dx = temperature gradient in the direction of heat flow in °C/m

K= coefficient of thermal conductivity of the material 

The negative sign indicates that heat flows in the direction of decreasing temperature. The coefficient of thermal conductivity of a substance is a physical property, which is defined as the ability of a substance to conduct heat. Thermal conductivity of a material depends upon chemical composition, state of matter. crystalline structures of a solid, temperature. pressure & whether or not it is a homogeneous material.

The heater will heat the rod on its end & heat will be conducted through the rod to be the other end. Since. the rod is insulated from outside, it can be safely assumed that the heat transfer along the copper rod is mainly due to radial conduction and at steady state the heat conducted shall be the cooling end. The heat conducted at steady state shall equal the heat absorbed by the water, thereby creating a temperature profile within the rod. The steady state heat balance at rear end of rod is:

or, QHeat transfer=QHeat transfer due to metal rod 

Thermal Heat conduction Apparatus:

The apparatus consists of one end of which is heated by an electric heater while other end of the rod projects inside the cooling water jacket. The middle portion of the rod is surrounded by a cylindrical shell filled with the alerts insulating powder. The temperature of rod is measured at different sections. The heater is provided with a dimmer stat through the jacket & its flow rate & temperature rise are noted by two temperature sensors provided at inlet & outlet of the water.

Procedure

First of all, continuous water supply was connected to the inlet of the water chamber and the outlet of the same chamber was connected to the empty pot aside. Then, the heat supplied was given to the chamber having rod at one end through the electric heat supplier. This was done until a steady state was achieved and all the sensors showed stable readings. As the heated rod was already connected with thermometer sensor at a certain interval of distance to get the temperature at each state. After that, the water supply was started to flow at low flow rate. The flow of water was measured using measuring cylinder and stopwatch simultaneous. After that, the temperature at different stage along with the outlet and inlet temperature were noted the observation table. After completion of this experiment, the thermal conductivity of metal rod was calculated for both observations.

Observation

Water inlet Temperature(T₇) =17.3℃

Water outlet Temperature(T₈) =18.3℃

Table 1: Observation table for water flow rate

Table 2: Observation table for Temperature Reading: 

Graph:   

From Graph: Slope obtained from graph( 𝑑𝑇 /𝑑𝑥) = 11 / 0.07 = 157.143

Calculation:

A = Cross sectional area of metal rod 

d = diameter of the rod

𝑑𝑇/𝑑𝑥 = slope of the graph between the length of the rod vs temperature

k= co-efficient of thermal conductivity of the metal rod

Q= heat gain by water

T=Temperature

v=volume of the water collected for flow measurement

x=length of the metal rod

T₇=water inlet temperature

T₈=water outlet temperature

Average volume per unit time=v/t=3.048ml/sec 

Result

The thermal conductivity of metal rod was found to be 165.756 watt/mK.

Discussion

In this experiment, the thermal conductivity of metal rod was determined. The thermal conductivity of metal rod was determined using the known value and by observing the required value from the thermal conduction apparatus in its steady state. During this experiment, heat transfer rate through the metal rod was same in every point on rod. All of the necessary readings for this experiment were obtained. After that, we had analysed the process of finding the thermal conductivity of metal rod. We learned that the calculated value of thermal conductivity from this experiment is error-full. The causes of errors were analysed. This error was due to certain equipment and observer's fault, unsteady state of temperature in metal rod and the problem in the steady flow of water in water supply pipe, very long time for the system to be steady and so on. Moreover, all the experiment was analysed and heat flow rate was studied efficiently.

Conclusion

From the experiment, the thermal conductivity of metal rod can be determined.

Precaution

By this experiment, we all are now familiar with the apparatus and the terms like temperature gradient, water flow rate, specific heat capacity with their practical applications and also the working procedure and all the precautions to be made. After the power supply is ON, it needs at least an hour to get in steady state of temperature. So, we should try to get the readings of the temperature of the steady state or nearer to the steady state. Also, we should check the water supply whether it is properly running or not. All the calculations should be made carefully and accurately.