# Thermal Conductivity – Resistance: Length

## Abstract

As described in part one, Thermal Conductivity is determined under steady state conditions by calculating the thermal resistance of a given material component. Thermal conductivity is, however; not the sole variable determining its value. In this experiment, a simple set-up will be used to determine the effect which component length has on heat flow and temperature difference on said component. This concept plays quite an important role in various industries such as the insulation industry

## Introduction

The goal of this experiment is to demonstrate the effect which varying length has on the thermal resistance of a given component. This will ultimately provide insight into the variables involved in heat flow and thermal resistance.

## Background Information and Equation

### Background Information

In a laboratory setting, Thermal Conductivity is derived by first calculating thermal resistance. From this thermal conductivity can be determine, however; if thermal conductivity is known, one can calculate the length of a given sample as well given its surface area.

Heat Flow Equation Q = ΔT / RΘ

• Q = Heat flow in Watts
• ΔT = Temperature difference in Degrees Celsius
• RΘ = Thermal Resistance (l / k ⋅ A)
• l = Length of a material in Meters
• k = Thermal conductivity constant in W/m-K
• A = Surface area in meters squared

This experiment will vary the bolded constant via different samples.

The design of this experiment is to observe the differences in temperature between components with varying length thus surface area, temperature difference and thermal conductivity must remain the same. It may be completed with non-metal samples, however; once again one may run the risk of a lengthy test time. In light of this metals are recommended and a table of various suitable metals can be found below.

Material Thermal Conductivity (W/m-K) Pricing Location of Purchase
Copper 397.48 ~12$for 10’ Amazon Aluminum 225.94 ~15$ for 32’ Amazon
Brass ~117.14 ~6$for 24’ Amazon ## Materials Material Price Location of Purchase Wiring (Same Diameter, 1.1m) •Copper •Aluminum •Steel Between 5-10$ each, 15-30$total. Amazon Candles x15 1$ Amazon
Infrared Thermometer 23$Amazon Beaker x2 (50ml) 3$ Indigo Instruments
Ruler 2$Amazon Hot Plate 15$ Amazon
Stop Watch 4$Amazon Total 63-78$ Amazon

## Experimental Set Up and Procedure

### Experimental Set Up

• Fill one of the four beakers with water and place it on the hot plate *make sure the hot plate is on a flat surface*
• Place the three remaining beakers parallel with one another at their respective distances (if distance d is 15cm then their distances will be: 15cm, 30cm, and 45 cm)
• Ensure the beakers are all level with one another by placing some stand underneath each beaker if needed

### Procedure

• Begin to boil the water on the hot plate
• While waiting for water to boil, cut three pieces of wiring with distances d, two times d and three times d. Bend the ends of the wires making ~50mm overhangs which will dip into the water and empty beaker.
• If using a distance d of 15cm, the total length of each wire will be 25cm, 40cm and 65cm.
• Optional: If wires are not used, rods (or any other sort of material) may be machined to have a 90° angle on one end.
• Cut an opening large enough for the width of the wire on the bottom of each candle and place the candle on the end of the wire which will be going into the empty beaker. Alternative: one could melt the bottom of each candle and let the wax mold to the end of the wire **this will require some time for the wire to cool in order to get accurate results**.
• Once the water has begun to boil, place all three wires with or without candles simultaneously across the beaker with water and the empty beakers. This may be done with gloves to prevent heat transfer from your hands to the wire.
• At this point, the beakers can be moved to the positions that follows (or desired)
• Wait 5-10 minutes
• Record the temperatures at the beginning and end of each wire and the degree to which the candles melted

## Observation

As with part 1, the temperature difference can be identified by one of two ways: the degree of melted candle at the tip of the wire or the temperature difference between wire tips and tails. The wire with the highest degree of melted candles at its tip is consider to have the most the smallest temperature difference. Should the experiment have occurred without problem, the shortest wire will have the highest degree of melted candle and the lowest temperature difference between tail and tip.

## Conclusion

It is to no surprise that the shortest wire will transfer the most heat across itself. Thermal Resistance is dependent on Length, Thermal Conductivity and Surface area. As length decreases so does Thermal Resistance and if the heat flow remained the same (as it should) the temperature difference must also decrease. The analogy of a road can be employed in this case. In order to reach from point A to point B, you have to travel along a road. The shorter the road the faster you will reach your destination, however; double that road and you require twice the time to make that journey. This concept as stated before plays an important role in the insulation industry. Instead of having a thin piece of insulation separating the inside of house from the outside, the insulation is thick. This slows the progression of heat from the inside out or the outside in and can save a lot of money.

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