EP015 TUTORIAL 1 PART 3

Physics 1

TUTORIAL
PART 3

Topic 11: Deformation of Solids
Topic 12: Fluid Mechanics
Topic 13: Heat Conduction and

Thermal Expansion
Topic 14: Kinetic Theory of Gases
Topic 15: Thermodynamics

PHYSICS UNIT_KMKJ

EP015 PHYSICS 1 1
11.0 DEFORMATION OF SOLIDS

TUTORIAL 11: DEFORMATION OS SOLIDS
LEARNING OUTCOMES

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STRESS AND STRAIN

1. Distinguish between stress and strain for tensile and compression force.
2. Discuss the graph of stress-strain for a metal under tension.
3. Discuss elastic and plastic deformation.
4. Discuss graph of force-elongation, f-e for brittle and ductile materials.

YOUNG’S MODULUS

5. Define Young’s Modulus.
6. Discuss strain energy from force-elongation graph.
7. Discuss strain energy per unit volume form stress-strain graph.
8. Solve problems relates to the Young’s Modulus.

BULK MODULUS

9. Define and use bulk modulus,
∆

= − (∆ )
10. Define and use compressibility,

1
=

EP015 PHYSICS 1 2
11.0 DEFORMATION OF SOLIDS

TUTORIAL 11.0: DEFORMATION OF SOLIDS

1. A wire P produces a strain of 6x10-4 when a load of 4kg is suspended at its

free end. Another wire Q, made from the same metal and having the same

length, has a diameter twice the diameter of P. Find the strain in Q if it is

suspended with a 4kg load. (1.5x 10-4)

2. Figure 1 shows the strain-stress curve for a given material. What are

a. Young’s modulus (75x1010Nm-2)
b. Approximate yield strength for this material (300x106Nm-2)

Figure 1

3. The Young's modulus is 1.50 x1010 N m-2 for a bone. The bone will fracture if
its stress is greater than 1.50 x108 N m-2 is imposed on it.

a. What is the maximum force that can be exerted on the femur bone in
the leg if it has a minimum effective diameter of 2.50 cm?

(73.65x103N)

b. If a 25.0 cm long bone is compressed, by how much will it be

shortened? (2.6x10-

3m)

4. A 30.0kg hammer with speed 20.0 m s-1strikes a steel spike 2.30cm in
diameter. The hammer rebounds with speed 10.0 m s-1 after 0.110 s. What is
the average strain in the spike during the impact? [ Y steel = 2.00 x1011 N m-2]

(9.86x10-5)

EP015 PHYSICS 1 3
11.0 DEFORMATION OF SOLIDS

5. A 2.0m long steel wire with a diameter of 4.00 mm is placed over a light

frictionless pulley as shown in Figure 1, with one end of the wire connected to

a 5.0kg object and the other end connected to a 3.00kg object as shown in

FIGURE 2. By how much does the wire stretch when the objects are in

motion? [ Y steel = 2.0 x 1011 N m-2] (2.92x10-5m)

Figure 2

6. A steel wire of length 4.7m and cross sectional area 3.0x10-5m2 stretches by

the same amount as a copper wire length 3.5m and cross sectional area of
4.0x10-5 m2 under a given load. What is the ratio of the Young’s modulus of

steel to that of copper? (1.79)

7. The force F against elongation e graphs for wire X and wire Y as shown in
FIGURE 3. The wires have the same original length and same cross sectional
area of 4.0 mm2.

i) Calculate the work done to extend wire X and wire Y by 1.0 mm. State which

wire is more rigid (Wx=0.1J, Wy=0.0625J)

ii) From the graphs above, calculate the ratio of the Young’ modulus of wire X

to the Young’ modulus of wire Y (1.6)

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11.0 DEFORMATION OF SOLIDS
8. A piece of bone under tension and compression as in FIGURE 4

FIGURE 4

a. Use the graph, calculate the Young’s modulus for bone under conditions of

compression and tension respectively. ( 1x109Nm-2, 1.75x109Nm-

2)

b. Given that the average cross sectional area of the bone is 6.0 × 10-4 m2 and

its length is 0.45 m.

i) By using this graph, calculate the compressive force at the instant the

bone breaks (1.2x104N)

ii) What is the reduction in length in the bone when the bone is just about to

break? (9mm)

iii) Calculate the energy stored in the bone when the bone is just about to

break. (54J)

9. The marina trench is located in the Pacific Ocean, and at one place it is nearly

eleven km beneath the surface of water. The water pressure at the bottom of

the trench is about 1.1x108 Pa. A steel ball of initial volume 0.32m3 is dropped

into teh ocean and falls to the bottom of the trench. What is the change in the

volume of the ball when it reaches to the bottom? Given the bulk modulus of

steel is 1.6x1011 Nm-2. (2.2x10-4m3)

10. Determine the volume contraction of solid copper cube, 10cm on an edge,

when subjected to a hydraulic pressure of 7.0x106Pa. Given the bulk modulus

of copper is 410Gpa. (5x10-8m3)

EP015 PHYSICS 1 1
12.0: FLUID MECHANICS

TUTORIAL 12: FLUID MECHANICS
LEARNING OUTCOMES

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HYDROSTATICS PRESSURE

1. Relate and use atmospheric pressure, gauge pressure and absolute
pressure.

BOUYANCY
2. Use diagram and hydrostatic pressure to explain buoyancy.
3. State and apply the Archimedes’ principle.

FLUID DYNAMICS
4. Illustrate fluid flow.
5. Explain and use continuity and Bernoulli’s equations

VISCOSITY
6. Define viscosity.
7. State and use Stokes’ law.
8. Sketch the graph of velocity-time, v-t to explain terminal velocity in liquid.

EP015 PHYSICS 1 1

Tutorial 12

Fluid Mechanics

1. 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 1
below.

12.0 cm h

oil C

A h
water
B

FIGURE 1

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

2. An iceberg of volume 40 m3 and density 920 kgm-3 is partially floating on the sea
water of density 1025 kgm-3. A helicopter of mass 4200 kg is then landing on the
iceberg. By using a suitable figure:

a) determine the percentage of the iceberg volume floats on the sea water before
the boy jumps on it.

b) does the helicopter immerse down into the sea?

3. An object is observed to be 300 N of weight in air and 200 N when the object is fully
immersed in a liquid of density 800 kgm-3. Determine :

a) the volume of the object.
b) the density of the object.

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4. A liquid of density 740 kgm-3 is flowing through a venturi meter as ashown in
FIGURE 2 below.

FIGURE 2
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.

5. 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.

Suggested Answers

1. (a) h = 10.2 cm (b) h = 0.18 cm

2. 10.24% (b)  = 2408kg m-3
3. (a) V = 0.0127 m3 (b) p = 32.65 Pa
4. (a) v1 = 4.2 cms-1 (b)  = 25.62 Pas (c) F = 0.29 N
5. (a) v = 0.06 ms-1

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13.0 Heat Conduction and Thermal Expansion

TUTORIAL 13: HEAT CONDUCTION AND THERMAL EXPANSION
LEARNING OUTCOMES

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HEAT CONDUCTION

1. Define heat conduction
2. Solve problems related to rate of heat transfer,


= − ( )
through a cross-sectional area (Maximum two insulated objects in series).
3. Discuss graphs of temperature-distance, T-x for heat conduction through
insulated and non-insulated rods. (Maximum two rods in series)

THERMAL EXPANSION

4. Define coefficient of linear, area and volume thermal expansion.
5. Solve problems related to thermal expansion of linear, area and volume

(include expansion of liquid in a container):
∆ = 0∆ ; = 2 ; = 3

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13.0 Heat Conduction and Thermal Expansion

TUTORIAL 13: HEAT CONDUCTION & THERMAL EXPANSION
1. Two metallic rods X and Y with similar length and cross-sectional area are joined together

and insulated. At steady state, the temperatures for rod X is 100°C and rod Y is 40°C at
each ends as shown in FIGURE 1. The thermal conductivity of X is twice of Y. Calculate the
temperature at the joint. [Ans: 80°C]

100°C XY 40°C
FIGURE 1

2. A glass window of cross-sectional area 1.50 m2 and thickness 0.20 cm is closed in winter.
The temperatures of the inner and outer surfaces of the window are 15°C and 0°C.
Calculate the rate of heat flow through the window. [Ans: 9.45 k Watt]

3. Determine the temperature gradient that must exist in a silver rod so that 100 W per square
meter of cross-sectional area can be transferred down the rod.
(Thermal conductivity of silver: 420 W m-1 °C-1) [Ans: -0.24 °C m-1]

4. The surface area pf a sheet of lead is 600 cm2 at 20°C. If it is heated to 90°C, determine
i. The change in the lead sheet surface area
ii. The new surface area of the lead sheet

(The coefficient of linear expansion of lead: 29 x 10-6 °C-1) [Ans: 2.44 x 10-4 m2, 602.44 x
10-4 m2]

5. A well insulated aluminium bar has 40 cm length and cross-sectional area 3.0 cm2. One of
its ends is maintained at a temperature of 130°C while its other end is kept at a temperature
of 10°C. If the bar in steady state condition, find
i. The temperature at a distance 10 cm from the end that is at 130°C
ii. The rate of heat flow through the bar

(Thermal conductivity of aluminium: 240 W m-1 °C-1) [Ans: 100°C, 21.6 Js-1]

6. A 100 cm rod A expands by 8.0 mm when heated from 0°C to 100°C. Calculate the
coefficient of linear expansion for rod A. [Ans: 80 µ °C-1]

EP015 PHYSICS 1 3
13.0 Heat Conduction and Thermal Expansion

7. A technician cuts a hole of area 2.0 cm2 through a copper sheet. The temperature of the
sheet rises to 150°C. Find the area of the hole when the sheet is cooled down to room
temperature 30°C. (The coefficient of linear expansion of copper: 1.7 x 10-5 K-1)
[Ans: 1.992 x 10-4 m2]

8. Two metal rods, steel and aluminium are clamped together on both ends as shown in

FIGURE 2 below. 0.30 mm

FIGURE 2
At 0°, both rods are each 30 cm and are separated by 0.30 mm at their unfastened ends.
Determine at what temperature the rods will just come into contact.

(The coefficient of linear expansion of steel: 1.1 x 10-5 °C-1, The coefficient of linear
expansion of aluminium: 2.4 x 10-5 °C-1) [Ans: 28.6°C]

9. A copper ball with a radius of 1.6 cm is heated to 353°C. The diameter of the ball has
increased by 0.18 mm. If the coefficient of volume expansion for the copper is 51 x 10-6 °C-
1, calculate the initial temperature of the ball. [Ans: 22°C]

10. A 60 liter steel tank is full of petrol at a temperature of 30°C. If the cover of the tank is not
tightened, how much petrol will spill out at 40°C? (The coefficient of linear expansion of
steel: 1.2 x 10-5 °K-1, The coefficient of volume expansion of petrol: 9.5 x 10-4 °K-1) [Ans:
5.48 X 10-4 m3]

EP015 PHYSICS 1 1
14.0 GAS LAWS AND KINETIC THEORY OF GASES

TUTORIAL 14: GAS LAWS AND KINETIC THEORY OF GASES
LEARNING OUTCOMES

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IDEAL GAS EQUATIONS

1. Solve problems related to ideal gas equation,
=

2. Discuss the following graphs of an ideal gas:
a. p-V graph at constant temperature
b. V-T graph at constant pressure
c. p-T graph at constant volume

KINETIC THEORY OF GASES
3. Discuss root mean square (rms) speed of gas molecules
4. Solve problems related to root mean square (rms) speed of gas molecules

MOLECULAR KINETIC ENERGY AND INTERNAL ENERGY

5. Discuss translational kinetic energy of a molecule,

3 3
= 2 ( ) = 2

6. Discuss internal energy of gas

7. Solve problems related to internal energy,

1
= 2

MOLAR SPECIFIC HEATS
8. Define molar specific heat at constant pressure, Cp and volume, CV

Use equation, Cp – CV = R and
= ( )

TUTORIAL 14: GAS LAWS AND KINETIC THEORY OF GASES

Please use these values in your calculations.

Universal gas constant R 8.31 J K-1 mol-1
Avogadro constant NA 6.02 x 1023 mol-1
Boltzmann constant k 1.38 x 10-23 J K-1

1. A fixed mass of an ideal gas is at pressure P. What will be the new pressure of the gas
if its temperature is halved and its volume is doubled?
A.
B.
C.
D.

2. Which of these graphs shows Gay-Lussac’s Law?

A V (m3) C P (Pa)

T (K) V (m3)
D V (m3)
B P (Pa)

T (K) T (K)

3. At certain temperature, the r.m.s speed of an ideal gas is . If the temperature of
the gas changed so that its pressure is doubled while the volume is kept constant, then
the root mean square speed of the molecules becomes:
A.
B.
C. √
D.

4. The pressure of a gas in a container of volume is . If the

temperature of the gas is , calculate the number of molecules in the gas.

A.

B.

C.

D.

5. Given an ideal gas, what is the energy for one degree of freedom for one molecule?
A.
B.
C.
D.

6.

a. Four closed tanks, A, B, C and D, each contain an ideal gas. The table gives

the absolute pressure and volume of the gas in each tank. If each tank has 0.2

moles of gas, calculate the temperature of the gas in each tank.

Absolute Pressure Volume
(Pa) (m3)

A 20 4

B 25 5

C 30 4

D 2.0 70

b. Sketch, write equations and the laws related to these graphs of an ideal gas:
i. p-V graph when the temperature is constant
ii. V-T graph when the pressure is constant

iii. p-T graph when the volume is constant
[132.96 K; 207.75 K; 199.44 K; 232.68 K ]

7.
a. State four assumptions related to the Kinetic Theory of Gases
b. Explain the root mean square speed of gas molecules

8.
a. Determine the root mean square speed at a temperature of 303 K for
i. hydrogen molecules
ii. nitrogen molecules

(given molar mass for hydrogen is 2 g mol-1 and for nitrogen is 28 g mol-1)

b. Determine the temperature at which the r.m.s speed of a helium molecule is
1.3 times greater than its speed at temperature 310 K.

c. The r.m.s speed of the atoms of a monatomic gas at a temperature of 20ºC is
603 m s-1. Find the mass of an atom of the gas.

d. What is the root mean square speed of oxygen molecules at 300 K?
(given molar mass for oxygen is 32 g mol-1)

[1.94 x 103 m s-1; 519 m s-1; 523.9 K; 3.3 x 10-26 kg; 483 m s-1]

9.

a. Find the mean kinetic energy of a molecule for an ideal gas at the following

temperatures.

i. 100 K

ii. 475 k

b. Determine the total internal energy for 4 moles of ideal monatomic gas at the

following temperatures.

i. 200 K

ii. 303 K

[2.07 x 10-21 J; 9.83 x 10-21 J; 9.97 x 103 J; 15.11 x 103 J]

10.

a. 3 moles of Helium gas is cooled down from its initial temperature of 600 K to
a final temperature of 300 K. Given Cv=2.98 J K-1 mol-1 and Cp= 4.97 J K-1
mol-1, calculate the heat released at

i. constant volume

ii. constant pressure

b. The quantity of heat absorbed by 1.2 moles of an ideal gas is 350 J. The gas
expands at constant pressure and the gas temperature rises by 25 K. Determine
the quantity of heat to be absorbed by the gas so that the temperature of the
gas can be increased by 10 K at constant volume.

c. The quantity of heat absorbed by three moles of an ideal gas is 150 J. The gas
expands at constant volume and the temperature rises from 273 K to 285 K. If
the ratio between constant pressure and constant volume is 3, determine the
molar heat capacity at constant pressure.
[-2682 J; -4473 J; 40.32 J; 12.5 J K-1 mol-1]

Ans: 2. B 3. C 4. A 5. A
1. D

EP015 PHYSICS 1 1
15.0 Thermodynamics

TUTORIAL 15: THERMODYNAMICS
LEARNING OUTCOMES

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FIRST LAW OF THERMODYNAMICS
1. State the first law of thermodynamics.
2. Solve problem related to first law of thermodynamics.

THERMODYNAMIC PROCESSES
3. Define the following thermodynamics processes:

a. Isothermal
b. Isochoric
c. Isobaric
d. Adiabatic
4. Discuss p-V graph for all the thermodynamic processes.
5. Determine the initial and final state for adiabatic process:

= ; −1 =
THERMODYNAMICS WORK
6. Discuss work done in isothermal, isochoric and isobaric processes.
7. Solve problem related to work done in

a. Isothermal process
b. Isobaric process
c. Isochoric process

EP015 PHYSICS 1 2
15.0 Thermodynamics

TUTORIAL 15: THERMODYNAMICS

1. 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
D. None Q, ΔU or W is necessarily zero

2. 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

3. The value of γ at constant pressure to that at constant volume is 1.40. 29.1 J of

heat is required to raise the temperature of 1 mol of gas by 1 K at constant

pressure. Calculate the molar specific heat of the gas at constant volume.

A. 40.7 J mol-1 K-1 C. 20.8 J mol-1 K-1

B. 37.4 J mol-1 K-1 D. 11.6 J mol-1 K-1

4. a) Write an expression representing
i) first law of thermodynamics and state the meaning of all the
symbols.
ii) work done by an ideal gas at variable pressure

b) 2500 J heat is added to a system and 1800 J work is done on the system.
Calculate the change in internal energy of the system. [4300 J]

EP015 PHYSICS 1 3
15.0 Thermodynamics

5. 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 p/ × 105 Pa B

A
4.0

b) BC path

c) CD path 2.0 C
d) DA path D

e) ABCDA path V /cm3

1.5 4.0

FIGURE 1

[1.0 J; 0; -0.5 J; 0; 0.5 J]

6. A fixed mass of gas initially at 7°C and a pressure of 1.00×105 N m-2 is
compressed isothermally to one-third of its original volume. It is then expanded
adiabatically to its original volume. Calculate the final temperature and pressure,
assuming γ = 1.40. [180 K; 0.644 x 105 Pa]

7. A sample containing 1.00 mol of the ideal gas helium undergoes the cycle of
operations as shown in FIGURE 2. BC is an isothermal process. Pressure at A
is at stp and pressure at B is 2.00 atm. Calculate

a) temperature at A [270 K]

b) temperature at B [540 K]

c) volume at C [44.8 x 10-3 m3]

P

B

C V
A

FIGURE 2

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15.0 Thermodynamics

8. A fixed mass of ideal monatomic gas is contained in a cylinder. The cylinder
volume can be varied by moving a piston in or out. The gas has an initial volume
0.010 m3 at 100 kPa pressure and its temperature is initially 300 K. The gas is
cooled at constant pressure until its volume is 0.006 m3.

a) Sketch a graph of pressure against volume for the above process.

b) Calculate the

i. final temperature of the gas [180 K]

ii. work done on the gas [-400 J]

iii. number of moles of gas [0.4 mol]

iv. change of internal energy of the gas [- 597.6 J]

v. heat transfer from the gas [-997.6 J]

9. FIGURE 3 shows a system undergoing a change from A to B following a path
of ACB. 90 J heat flows into the system. 70 J of work is done by the system.

FIGURE 3

a) Calculate the heat flows into the system that follows the path of ADB
when the work done by the system has a value of 15 J. [35 J]

b) When a system reversing its path to A by a curve path, the amount of
work done by the system is 45 J, decide whether the system gains or
loses heat and determine its value. [- 65 J]

c) When UA = 0 and UD = 8 J, evaluate the amount of heat gains during
the process A → D and D → B. [23 J; 12 J]

EP015 PHYSICS 1 5
15.0 Thermodynamics

10. An ideal gas of fixed mass initially of volume 3.0×10-3 m3 at 17°C undergoes the
following changes:

I. The temperature increases to 27°C at constant pressure. 20.5 J heat is
supplied.

II. The temperature is reduced to the initial temperature of 17°C at constant
volume.14.6 J heat is released.

III. The gas is then compressed adiabatically slowly until the volume is
2.0×10-3 m3.

a) Show these processes in a graph of pressure p against volume V.
b) Calculate the gas temperature in the final process (iii) [346 K]