THERMAL PHYSICS LABORATORY
Dr.Nourhan Kawni
Dr.Salem Marhaba
Student: Roua Etry ID: 202203078
Experiment4: Mechanical Equivalent of Heat
Aim of the experiment:
Determination of the mechanical equivalent of heat.
Theory:
Mechanical energy from friction is fully converted into thermal energy. As both forms of
energy are given in the same unit of 1J=1 N.m, and as heat is a form of energy, the total
amount of mechanical energy must be transformed into an equal amount of heat energy
according to the law of conservation of energy. Thus, the mechanical equivalent of heat
must amount to:
∆𝑊/∆𝑄 = 1
In this experiment, a metallic body is rotated and heated.
As the cylinder turns, the friction between the cylinder and the rope converts the work into
thermal energy, which raises the temperature of the cylinder.
The work due to friction on the cylinder:
W = 2πn(F2 − F1 )

The work is converted into thermal energy:
Q = crm(T2 − T1 )
Where:
Q: heat
W: work done due to friction
n: number of rotations
C: specific thermal capacity of the cylinder
r: radius of cylinder
m: mass of the cylinder
F1: weight of the object = 10 N
T2: final temperature
F2: force on the spring
T1: initial temperature of the cylinder
Apparatus:
1. Friction cylinder CuZn, m = 1.28 kg, m = 0.64 kg (C= 385 j/kg.C)
2. Friction cylinder Al, m = 0.39 kg (C= 900 J/Kg.C)
3. Plastic friction band
4. Crank handle
5. Thermometer
6. Thermally conducting paste
7. Screw clamps
8. Spring balance 10 N
9. Commercial weight 1kg
Method:
1- Fix the friction cylinder and the crank handle to the journal bearing
2- Hang a spring balance from the holder.
3- Attach the friction band to the spring balance.
4-Wrap the band 2.5 times around the cylinder so that the
load on the balance is relieved if the crank handle is turned
to the right.
5-Attach a weight to the lower end of the friction band.
6-To measure temperature, the thermometer is held with a
universal clamp and carefully introduced into the bore hole
of the friction cylinder. The thermometer and the bore hole
of the cylinder must be carefully aligned, so the
thermometer will not break while the cylinder is rotating.
To improve thermal contact, the bore hole is filled with
heat conducting paste.
7-The temperature of the cylinder should be measured
before and after a given number (25, 50) of rotations.
Notice: For small and large friction cylinder CuZn, the
specific thermal capacity c is equal to 385 J/KgC. whereas c
for friction cylinder Al is equal to 900 J/kgC.
8-After collecting the measurements calculate Q and W and
then the mechanical equivalent of heat.
Data & Calculations:
F1=10 N
r=2.45cm
CuZn(small)
T1=20℃
25
50
rotations
rotations
T2(C)
20.3
22.5
CuZn(large)
T1=22℃
25
50
rotations
rotations
22.2
21.5
Al
Cylinder
Spring
balance
CuZN
Cylinder
Crank
handle
Plastic
friction
band
Thermometer
Commercial
weight
Fig 1
Al
T1=20.5℃
25
rotations
20.6
50
rotations
21
F2(N)
53
50
51
53
42
40
W(J)
165.48
308.876
157.78
330.966
123.15
230.9
Q(J)
123.2
542.08
98.56
246.4
70.2
140.4
∆W/∆Q
1.3
0.6
1.6
1.3
1.7
1.6
Table 1
Conclusion:
1. First conclusion we can take from table 1 is that both work and heat increase when
increasing the number of rotations.
2. The mechanical equivalent of heat is always around 1 (the only reason it's not equal to
one is experimental errors and that's normal considering that this experiment is not easy to
execute), which means that most of work is converted into heat.