EP015 Physics Tutorial

A The strip expands vertically.
B The strip does not expand at all.
C The strip bends to the left side.
D The strip bends to the right side.

5. A small steel ball of temperature 120oC is touched to a bigger copper ball of
temperature 70oC. Which of the following statements is CORRECT?

A Heat will be transferred from the steel ball to the copper ball.
B Heat will be transferred from the copper ball to the steel ball.
C Heat will be transferred each other with the same rate.
D No heat will be transferred at all.

SECTION B

1. A copper wire (Ycopper = 120 GPa) and a tungsten wire (Ytungsten = 360 GPa) are
dimensionally identical. The length and the diameter of the wires are 15.0 m and
5.0 mm. If the wires respectively hang a load of mass 20.0 kg.

a) Determine the stress of both wires.
b) Determine the elongation of copper and tungsten.
c) Determine the strain of both wires.
d) Determine the percentage of elongation of both wire.
e) Which wire is harder?
f) Determine the ratio of elongation of copper to that of tungsten.
g) Sketch the graph of force against elongation for the both wires.
h) Sketch the graph of stress against strain for the both wires.
i) Determine the strain energy of both wires.
j) Determine the strain energy per unit volume of both wires.

(ANS :a) copper = tungsten = 10.0 x106 Nm-2, b) xcopper = 1.25 mm, xtungsten =
0.42 mm, c) copper = 8.3 x10-5, tungsten = 2.8 x10-5,d) %copper = 0.0083%,

%tungsten = 0.0028%, f) 3, i) Ucopper = 0.123 J, Utungsten = 0.041 J, j) U/Vcopper =
418 Jm-3, U/Vtungsten = 139 Jm-3)

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2. A U-shape tube is filled with water (water = 1000 kgm-3) at one end and a small

amount of cooking oil (oil = 850kg m-3) at the other end as shown in FIGURE 8.2
below.

12.0 cm h

oil C

A h
water
B

FIGURE 8.2

Based on the figure, if the length of the oil is 12.0 cm determine :
a) the length h.
b) the difference level, h.

(ANS : 10.2 cm, 0.18 cm)

3. A liquid of density 740 kgm-3 is flowing through a venturi meter as ashown in
FIGURE 8.3 below.

FIGURE 8.3
If the radius of r1 = 40.0 cm and r2 = 15.0 cm and velocity v2 = 0.3 ms-1,
determine :
a) the velocity v1.
b) the pressure difference, p between the two point.

(ANS : 4.2 cms-1, 32.65 Pa)

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4. A steel ball of diameter 2.0 cm and density 7900 kgm-3 falls vertically in a cup of
liquid of density 850 kgm-3 and depth 20.0 cm in 3.3 s. By using a suitable figure,
determine :

a) the terminal velocity of the ball.
b) the viscosity of the liquid.
c) the viscous (frictional) force due to the liquid on the ball.

(ANS : 0.06 ms-1, 25.2 Pas , F = 0.29 N)

5. Two identical rods respectively are made of copper and iron. The length of the
rods is 20.0 cm and cross-sectional area of 3.5 cm2. One end of both rods is
maintained at temperature of 80oC. The thermal conductivity of copper is 400
Wm-1K-1 and of iron is 70 Wm-1K-1. If the other end of the both rods is
maintained at 27 oC, by using a suitable figure, determine :

a) the heat flows through the copper rod in 1 minute.
b) the heat flows through the iron rod in 1 minute. What conclusion can be

made?
(ANS : 2226 kJ, 390 J)

6. A metal rod is made of copper and iron of equal cross-sectional area and length,
joins end to end with the copper end maintained at a temperature of 100oC while
the iron end is maintained at 20oC. The thermal conductivity of copper is 400
Wm-1K-1 and of iron is 70 Wm-1K-1. The rods are well lagged.

a) By using suitable figure, determine the steady state temperature at the
adjoin.

b) Sketch a graph to show how the temperature varies with distance along
the copper and iron.
(ANS : Tadjoin = 88.1 oC)

7. A 50.0 cm long copper tube of external diameter 2.5 cm and thickness 1.4 mm at
27oC as shown in FIGURE 8.3 below is heated to 90oC. The coefficient of linear
expansion for copper is 1.7 x10-5 K-1. Determine :

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1.4 mm 0.5 m
cm mm

2.5 cm
mm

FIGURE 8.3

a) the length of the rod at 90oC.
b) the external diameter of the rod at 90oC.
c) the internal diameter of the rod at 90oC
d) the area of the rod at 90oC (excluding the hollow area).

(ANS : L = 50.054 cm, d = 2.503 cm, d'’ = 2.2224 cm, A = 1.042 cm2)

8. A copper kettle contains full of water at 27oC. When the water is heated to its
boiling point, the volume of the kettle expands by 1.2 x10-5 m3. If the coefficient
of volume of copper is 1.5 x10-6 oC-1 and of water is 207 x10-6 oC-1, determine :

1. the volume of the kettle at 27oC.
2. the volume of the water displaced out from the kettle at the boiling point

(ANS : Vkettle = 0.1096 m3, Vwater = 1.66 x10-3 m3)

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TOPIC 9 : KINETIC THEORY OF GASES AND THERMODYNAMICS

9.1 KINETIC THEORY OF GASES
9.2 MOLECULAR KINETIC ENERGY AND INTERNAL ENERGY
9.3 MOLAR SPECIFIC HEAT
9.4 FIRST LAW OF THERMODYNAMICS
9.5 THERMODYNAMICS PROCESSES
9.6 THERMODYNAMICS WORK

At the end of this topic, students should be able to:

9.1 KINETIC THEORY OF GASES

1. State the assumptions of kinetic theory of gases.
2. Describe root mean square (rms) speed of gas molecules, = √< >
3. Solve problems related to root mean square (rms) speed of gas molecules.

9.2 MOLECULAR KINETIC ENERGY AND INTERNAL ENERGY
4. Discuss translational kinetic energy of a molecule,

5. Discuss internal energy of gas.
6. Solve problems related to internal energy,

9.3 MOLAR SPECIFIC HEAT
7. Define molar specific heat at constant pressure, and volume,

8. Use equation, − = and =


9.4 FIRST LAW OF THERMODYNAMICS

9. State the First Law of Thermodynamics, ΔU = Q – W
10. Solve problem related to First Law of Thermodynamics.

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9.5 THERMODYNAMICS PROCESSES
11. Define the following thermodynamic processes:
i. isothermal;
ii. isochoric;
iii. isobaric; and
iv. adiabatic.
12. Analyse p-V graph for all the thermodynamic processes.
13. Determine the initial and final state for adiabatic process:
PV = constant and −1=constant

9.6 THERMODYNAMICS WORK
14. State work done in isothermal, isochoric and isobaric processes.
15. Solve problem related to work done in:

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KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TOPIC 9
(KINETIC THEORY OF GASES AND THERMODYNAMICS)

SECTION A

1. A diatomic gas is at temperature of 400K. What is the mean kinetic energy of each

of these molecules?

A. 4.14x1020 J C. 4.14x10−20 J

B. 1.38x10−20 J D. 2.07x1020 J

2. The following statements are the kinetic theory of gases EXCEPT
A. there is intermolecular forces during collisions.
B. the gas molecules move haphazardly and randomly.
C. molecular collisions are elastic.
D. the molecular motion was affected by its mass and velocity.

3. 10g NO2 occupies 4.0x10−5 m3 at a temperature of 450K. Calculate the
pressure of the gas.

A. 5.61x109 Nm−2 C. 1.56x107 Nm−2

B. 2.03x107 Nm−2 D. 4.30x108 Nm−2

4. The first law of Thermodynamics may be written in the form of equation
Q =ΔU + W where Q is the energy supplied to a gas, ΔU is the increase in its
internal energy and W is the work done by expansion. When a real gas undergoes
a change at constant pressure which of the following statements is TRUE?
A. Q is necessarily zero
B. ΔU is necessarily zero
C. W is necessarily zero

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D. None Q, ΔU or W is necessarily zero

5. In an adiabatic process, the internal energy of a system of gas s decreases by 800J.
Which of the following statements is CORRECT?
A The system lost 800 J by heat transfer to its surroundings
B The system gained 800 J by heat transfer from its surroundings
C The system performed 800 J of work on its surroundings
D The surroundings performed 800 J of work on the system

SECTION B

1. a) State the assumptions of the kinetic theory of gases
b) If the mean square speed of the molecules at temperature To and pressure
po is v0 , calculate the new mean square speed , v when the temperature is
raised from 100 oC to 200 oC.
(ANS: v = 1.27v0 )

2. A vessel of volume 30 liters contains 2.5 moles of gas at 30ºC.
a) Calculate the gas pressure.
b) If the gas is neon, calculate the mass of the gas in the vessel.
[Molar gas constant = 8.31J mol K ; relative atomic mass of neon = 40]
(ANS: 2.1 x 105 Pa, 0.10 kg)

3. The mass of nitrogen (N2) gas in a container at STP is 120 g. If the gas is compressed
at pressure 10 atm, the temperature of the gas increases to 200 °C. Calculate the
initial and final volume of the gas.
( Mass of 1 mole of N2, gas is 28 g)
(ANS: 9.63 x 102 m3)

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4. A chamber is filled with 25.0 moles of helium gas at 200 oC.
a) Calculate the internal energy of the system
b) Explain what happens to the degree of freedom if the temperature
increases.
c) If the helium gas is replaced with 10 moles of nitrogen (N2) gas, determine
the difference between the internal energy of helium and nitrogen gases.
( N A = 6.02 10−23 molecules mol-1 , k = 1.38 10−23 JK −1 )
(ANS: 1.47x105 J , 48.8 x 103 J )

5. An idea diatomic gas is cooled from 260C to 100C at constant pressure of 1 atm. If
there are 1200 moles of the idea gas, what is the change in internal energy of the
gas?
(ANS: -4.00 x 105 J)

6. (a) State the First Law of Thermodynamic.
(b) In an isobaric process, an unknown gas expands from an initial volume of 4 L
to a final volume of 18 L at a constant pressure of 10 kPa.
(i) How much work is done by the gas?
(ii) What is the change in internal energy of the gas if 10 J of heat flowed
out during the process?
(iii) Sketch the P-V graph for the process.
(ANS: -140 J, -150 J)

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7.

p/ × 105 Pa B

A
4.0

2.0 C
D

1.5 4.0 V /cm3

FIGURE 1

The p-V diagram in FIGURE 1 applies to a gas undergoing a cyclic change in a
piston-cylinder arrangement. Calculate the work done by the gas in
a) AB path
b) BC path
c) CD path
d) DA path
e) ABCDA path

(ANS: 1.0 J, 0 J, -0.50 J, 0 J, 0.50 J)

8. The initial and final temperatures of 2 mol of helium gas are 300 K and 600 K

respectively. Find the heat absorbed by the gas at

(a) constant volume.

(b) constant pressure.

[ = 2.98 J mol-1 K-1, = 4.17 J mol-1 K-1]

(ANS: 1788 J, 2502 J)

9. Sketch on the same axes the p-V graph for each of the following processes:
• Isobaric
• Isothermal
• Adiabatic

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10. A container contains 0.4 m1 of gas at 30 0C and 2 atm. The gas is compressed
isothermally to hall its original volume and then the gas is allowed to expand
isobarically back to its original volume.
(i) With the same axes, sketch and label p- V graphs for these two
processes.
(ii) Determine the pressure of the gas after the isothermal compression.
(iii) Determine the final temperature of the gas.
(iv) What is the work done for the whole processes?
(ANS: 4 atm, 333 0C, 2.5 x 104 J)

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