Unit 6 Thermal Conductivity
Objectives
To measure the thermal conductivity coefficients of several different materials by
thermal conductivity apparatus.
Apparatus
Steam stove, thermal conductivity apparatus, measuring cup, electric scale,
thermometer, polystyrene cover, samples, timer (stopwatch), clamps.
Cover the ice with the can
Clamp this tube
Measuring cup B
Fill to 60%~70%.
Light D
Measuring cup A
Knob C
Principles
1. In a stable and uniform heat conduction, the transmitted heat ∆Q within time
∆t is proportional to the temperature difference, cross sectional area A
(perpendicular to the direction of heat flow), and the inverse of thickness 1/h.
The proportion factor is the thermal conductivity. As shown in Eq. (1)
kA∆T∆t
……………………(1)
h
where ∆Q is the total transmitted heat,
∆Q =
∆T is the temperature difference,
∆t is the time interval,
A is the cross sectional area,
h is the heat transmission distance (the thickness of the sample), and
k is the Thermal Conductivity.
2. In this experiment, we keep one end of the sample at 100 ℃ and the other end at
0 ℃. i.e. ∆T = 100 ℃. ………….(2)
Q1: How to maintain the temperature of the two ends at 100 ℃ and 0 ℃?
3.
In this experiment, we measure the melt rate of ice to determine the rate of heat
conduction. Latent heat of ice is 80 cal/g, and then in Eq. (1) ∆Q =mass of
melting ice m (g) × 80 (cal/g) ……… (3).
Substitute Eq. (2) and (3) to Eq. (1), we have
80 × m × h ⎛
Cal
⎞
⎜
⎟.
A × 100 × ∆t ⎝ cm ⋅ °C ⋅ sec ⎠
( h is in unit of cm )
k=
Instructions
1. Set up your devices as Fig. 1, but do not connect the steam stove.
2. Measure the thickness h of the sample.
3. Connect the steam stove when the steam is ready, and use measuring cup B to
4.
5.
collect the water from the steam chamber.
Place your sample on the top of the steam chamber and tight the screw to fasten
the sample, just as Fig.1. Aim the escape canal at the drain, and you can put on
some petrolatum (Vaseline) to prevent leakage.
Wait for a couple minutes for the system to become stable so that the temperature
will stop rising.
6. Place the plastic can (with ice inside) under tap (faucet) and pour it with tap
water ( just pour the external surface of the can, and DO NOT pour the water
inside the can). Rotate the can when pouring tap water on it, hence the can will
be heated uniformly ( DO NOT pry out the ice).
Q2: Why don’t we pour the tap water directly on the ice but on the external surface of
the can?
7. Put the ice ( with the plastic can) upside-down on the V-type escape canal of the
sample.
8. Wait for a few minutes until the ice starts melting and the surface of ice totally
contacts the sample. NOTE: The temperature of ice may be under 0 ℃ before
the ice starts melting, so we have to wait and start our experiment after it starts
melting. If the surface of ice is not smooth, you may have to grind it.
9. Measure the weight of measuring cup A.
10. Measure the diameter d1 of the ice.
11. Measure the mass of water collected in measuring cup A after a recommended
time of 5 minutes, and record the time as t1. Then measure the diameter d2 of the
2
ice. d avg
1
⎛1
⎞
= (d 1 + d 2 ) , A = π ⎜ davg ⎟ .
2
⎝2
⎠
12. Measure the total mass of measuring cup A. Then subtract the mass measured in
step 9 from the total mass and record the value as m1. Then the heat absorbed by
the ice is ∆Q1 = m1 × 80 . Then pour out the water from cup A.
13. Add a polystyrene under the ice.
14. When the ice is melting steadily, start colleting the water with measuring cup A.
After a recommended time of 5 minutes, subtract the mass measured in step 9
from the total mass of the cup, and record it as m2. The heat absorbed by the ice
is ∆Q 2 = m 2 × 80 .
15. If t1=t2, ∆Q1 − ∆Q 2 =
kA∆T∆t
h
(m1 − m2 ) × 80 .
, where ∆t = t1 . k =
h
100 × A × ∆t
NOTE: A reasonable error should be under 15%.
Q3: Why do we have to measure ∆Q1 and ∆Q2 ? What will it be if we only do it once
(without measuring ∆Q2 )?
Q4: How to calculate for k when t1 ≠ t2 ?
16. Repeat step 9 to 14.
17. Change a sample and repeat step 9 to 15.
Remark:
1. The steam stove and steam chamber are extremely hot, be careful when
operating your experiment!
2. Fill the stove to up to 60% to 70% is enough. Too much water will decrease the
3.
4.
5.
heating; on contrary, you may have to add some water during the experiment if
the water is not enough.
When all the devices are ready and you are going to start your experiment, you
can turn the switch C to “MAX”.
The glass sample may break if the heating is not uniform. Therefore, you can
pour some cold water on the glass before placing it on the heat conductivity
apparatus. Also, you can slide the ice on the glass sample to make the
temperature uniform. Place the ice by the V-type escape canal after all.
When D light blinks, you have to turn off the stove and add some water into it to
prevent damage.