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4.1.4 Temperature Scale

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Calibrating a Thermometer

  1. To calibrate a thermometer means to put the correct mark of reading at the correct place so that other temperature can be deduced from these marks. 
  2. To do this, two extreme points are chosen to mark its scale and these points must be able to be reproduced accurately.
  3. Usually, we take the steam point of pure water as 100°C and the ice point of water as 0°C.
    To calibrate a thermometer, the ice point of water is usually taken to be 0°C  
    To calibrate a thermometer, the steam point is taken to be 100°C

  4. After determining the position of the ice point and steam point, the temperature of an object can be determined by using the formula:

Example 1:
The length of the mercury column in a non-calibrated mercury thermometer is 2cm when its bulb is immerse in melting ice and 20cm when the bulb is in steam above boiling water. What would the temperature be is the length of the mercury column is 11cm?

Answer:
l0°C = 2cm
l100°C = 20cm
lθ = 11cm




Example 2:
The length of the alcohol column in a thermometer is 2.5cm and 17.5cm when the thermometer is dipped into a melting ice and a boiling water respectively. Find the distance between every 10°C of the scale on the thermometer.

Answer:
Distance for 100oC = 17.5cm – 2.5 cm = 15.0cm

Distance for 10oC = 17.5cm – 2.5 cm
= 15.0cm ÷ 10 = 1.50 cm


Example 3:


Figure above shows the length of the mercury thread of a thermometer at melting point and boiling point of water. What is the length of the mercury thread when the thermometer is dipped into a hot liquid of temperature 70°C?

Answer:


Absolute Zero and the Kelvin Temperature Scale

  1. Absolute temperature is the temperature measured in Kelvin scale, which it is a temperature reading made relative to absolute zero.
  2. We can convert a temperature in °C to absolute temperature by adding 273 to the temperature.
    For example:
    25°C = 273 + 25 = 298 K
    100°C = 273 + 100 = 373 K
  3. Absolute zero is the temperature where thermal energy is at minimum. It is 0 on the Kelvin scale and -273 on the Celsius scale.

 

4.1.3 Thermometer

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Liquid in Glass Thermometer

  1. Liquid in glass thermometer works on the principle that liquid expands as the temperature increases and contracts as the temperature decreases.
  2. The most commonly used liquids in such thermometers are
    1. Mercury
    2. Alcohol

Q & A

Q: State the advantageous and disadvantageous of using mercury as the liquid in a liquid in glass thermometer.

A:
Advantageous:
  1. Doesn’t wet the wall of the capillary tube.
  2. Can be seen easily
  3. Expand uniformly when heated
  4. Good heat conductor

Disadvantageous:
  1. Freezing point = -39°C. Not suitable to measure temperature lower than -39°C.
  2. Poisonous
  3. Expensive

Q & A

Q: State the advantageous and disadvantageous of using alcohol as the liquid in a liquid in glass thermometer.

A:
Advantageous:
  1. Freezing point = -115°C. Suitable for measuring low temperature.
  2. Expands greater than mercury.

Disadvantageous:
  1. Transparent. Difficult to be seen. Need to be coloured.
  2. Always cling the wall of the capillary tube.
  3. Has tendency to break the tube at high temperature.


Q & A

Q: State the characteristics of the liquid used in a liquid in glass thermometer.

A:
  1. Easily visible
  2. Good conductor of heat
  3. Expand and contract rapidly over a wide range of temperature
  4. Does not cling to the wall of the capillary tube of the thermometer.

Q & A

Q: State and explain how the sensitivity of a liquid in glass thermometer can be increased.
A:
  1. The sensitivity of a mercury thermometer can be increased by using a smaller mercury bulb, thinner wall and smaller bore.
  2. A smaller bulb contains less mercury and hence absorbs heat in shorter time. As a result it can response faster to temperature change.
  3. A glass bulb with thinner wall can transfer heat to the bulb easier. Therefore, the thermometer can response quickly to small changes of temperature near the surrounding.
  4. Capillary with narrow bore produces a greater change in the length of the mercury column. Therefore a small change in temperature can be detected easily.

 

4.1.2 Thermal Equilibrium

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  1. Two objects are in thermal contact when heat energy can be transferred between them.
  2. Two objects are in thermal equilibrium when there is no net flow of heat between two objects that are in thermal equilibrium.
  3. Two objects in thermal equilibrium have the same temperature.
Example:
Figure below shows 2 blocks in thermal contact with each other. Initially, the temperature of the 2 blocks are different, and there is a net flow of thermal energy from higher temperature to lower temperature.

After some time, thermal equilibrium achieved, where the temperature of the 2 blocks become the same, and there is no net flow of thermal energy between the 2 blocks.

Before
  1. Initially, the temperature of block A is higher than block B.
  2. The rate of thermal energy transfer is higher from block A to the block B (1000J/s).
  3. There is also thermal energy transfer from the block B to block A, but with lower rate (only at 200J/s).
  4. Therefore, there is a net heat flow of thermal energy from the block A to block B.
  5. As a result, the temperature of block A decreases whereas the temperature of B increases.
After
  1. Thermal Equilibrium Achieved. 
  2. The temperature of the 2 blocks become the same.
  3. Heat flow is still goes on between the blocks.
  4. However, the rate of flow of heat are equal in both direction. As a result, the net heat flow is equal to 0.

Objective Question:
2 iron blocks, P and Q are in thermal contact. The initial temperature of P and Q are 10°C and 50°C respectively. Which of the followings is true when P and Q are at thermal equilibrium.
  1. The temperature of P will be higher than the temperature of Q.
  2. The net flow of heat between P and Q is zero
  3. The temperature of P and Q will be lower than 50°C but higher than 10°C.
  4. There is no heat flow between the 2 blocks.

 Answer:
The correct answer is II and III.

Answer I. is incorrect.
When 2 objects achieve thermal equilibrium, the temperature of the 2 objects will be the same.

Answer II. is correct.
When 2 objects achieve thermal equilibrium, the rate of flow of heat is equal, hence there is no net flow of heat between the 2 objects.

Answer III. is correct.
When P and Q are in thermal contact, the temperature of P (10°C)will increase whereas the temperature of Q (50°C) will decrease. When P and Q are in thermal equilibrium the temperature of P and Q will be the same and the temperature will be higher than 10°C but lower than 50°C.

Answer IV. is incorrect.
In thermal equilibrium, there is still heat flow between P and Q.

However, the rate of the heat flow is equal in both direction (P to Q and Q to P), hence the net flow of heat between P and Q is zero.

Applications of Thermal Equilibrium

Oven

  1. When food such as meat or cake is put in the oven, the heat of the oven is transferred into the food.
  2. This process will continue until the food is in thermal equilibrium with the air in the oven.
  3. This happen when the temperature of the food is equal to the temperature of the air in the oven.

Refrigerator

  1. When food is put in the refrigerator, the heat from the food is transferred into the air of the refrigerator.
  2. This process is continued until the temperature of the food  equal to the temperature of the air in the refrigerator, when thermal equilibrium is reached between the food and the refrigerator.

Thermometer

  1. Thermometer is placed in contact with the patient’s body.
  2. If both the body temperature of the patient and that of the mercury (or alcohol) in the clinical thermometer have reached thermal equilibrium, then the temperature of the thermometer is the same as the body temperature, hence the reading of the thermometer shows the body temperature of the patient.

 

4.1.1 Heat and Temperature

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  1. Heat is the flow of thermal energy.
  2. Temperature is a measure of the average kinetic energy which each molecule of an object possesses.

Thermal Energy and Heat

  1. Thermal energy is a measure of the sum of kinetic and potential energy in all the molecules or atoms in an object.
  2. The SI unit of thermal energy is Joule, J.
  3. Heat is the flow of thermal energy, from a hotter body to a colder one.

Temperature

  1. Temperature is a physical quantity which measures the degree of hotness of an object.
  2. Temperature is a measure of the average kinetic energy which each molecule of an object possesses.
  3. One object is at a higher temperature than another if the average kinetic energy of each of its molecules is greater. 
  4. The SI unit of temperature is Kelvin, K.

Differences between Thermal Energy and Temperature

Thermal Energy
Temperature
A form of Energy Degree of hotness of an object.
Unit: Joule (J) Unit: Kelvin (K)/ Degree Celsius (oC)
Sum of the kinetic energy and potential energy of the particles. Average kinetic energy of the particles.
Derived quantity Base quantity

 

3.6.2 Applications of Bernoulli’s Principle

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Aeroplane

  1. When a wing in the form of an aerofoil moves in air, the flow of air over the top travels faster and creates a region of low pressure. The flow of air below the wing is slower resulting in a region of higher pressure.
  2. The difference between the pressures at the top and underside of the wing causes a net upward force, called lift, which helps the plane to take-off.

Q & A

Q: Explain how an upthrust is produced when the aeroplane is moving.

A:
  1. When the aeroplane is moving, air flows faster above the wing than below.
  2. Therefore, the air pressure below the wing is higher than above.
  3. The difference in air pressure produces a net force acting upwards.

Q & A

Q: There are slat in front and flaps at the back of the wings of an aeroplane. Describe with the aid of a diagram how the slat and flaps of the wings help in lifting the aeroplane when the aeroplane starts to depart.
A: 
  1. When the aeroplane starts to depart, the slat and flaps are stretched and spread out to increase the surface area of the wings.
  2. This increases the lifting force acting on the aeroplane.

Sports

In some of the sport such as football, a player can make the ball move in a curve path by spinning the ball. This effect can be explained by Bernoulli's Principle.

Insecticide Spray

 

  1. When the plunger is pushed in, the air flows at a high velocity through a nozzle.
  2. The flow of air at high velocity creates a region of low pressure above the metal tube. The higher pressure of the atmospheric air acts on the surface of the liquid insecticide causing it to rise up the metal tube.
  3. The insecticide leaves the top of the metal tube through the nozzle as a fine spray.

Bunsen Burner

  1. When the burner is connected to a gas supply, the gas flows at high velocity through a narrow passage in the burner, creating a region of low pressure.
  2. The outside air, which is at atmospheric pressure, is drawn in and mixes with the gas.
  3. The mixture of gas and air enables the gas to burn completely to produce a clean, hot, and smokeless flame

Carburetor

A carburetor is a device that blends air and fuel for an internal combustion engine. Figure above shows how Bernoulli's principle is applied in a carburetor to mix the air with the fuel.

Q & A

Q: Explain why 2 fast moving boats tend to move closer to each other.

A: 
  1. When the two boats travel at high speed, the stream of fluid (air and water) between the boats flow faster than the other sides of the boats.
  2. This form a low pressure zone in between the boats.
  3. The higher pressure at the other sides of the boat pushes the boats closer to each other.

 

3.6.1 Bernoulli’s Principle

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Bernoulli's Principle states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases.


Venturi Effect

The Venturi effect is the fluid pressure that results when an incompressible fluid flows through a constricted section of a pipe.

Experiment 1

Figure above shows that when water flow from left to right, the water level decreases from left to right. This indicates that, the water pressure decreases from left to right.

Explanation:
Liquids flow from places with higher pressure to places with lower pressure.


However, if the experiment is repeated by using a Venturi tube where the diameter at B is made smaller than A and C as in the diagram above, the water level become lowest at B.

Explanation:
The pressure at B is the lowest because the liquid flow the fastest at B. According to Bernoulli's Principle, the faster the water flow, the lower the water pressure.


Experiment 2


Figure above shows some air is blow through a tube from left to right. The water level in the capillary tube increases from left to right.
This indicates that the pressure in the tube decreases from left to right.

Explanation:
Gases flow from places with higher pressure to places with lower pressure.


However, if the tube is replaced by a Venturi tube, the water level become highest at B. This indicates that, the pressure of the air is the lowest at B.

Explanation:
The pressure at B is the lowest because the gas flow the fastest at B. According to Bernoulli's Principle, the faster the gas flow, the lower the gas pressure.

Experiment 1

A paper will be lifted upwards when air is blown rapidly above it.

Explanation:
  1. Air move rapidly above the paper, causes the pressure above the paper to decrease.
  2. Pressure below the paper becomes relatively higher.
  3. Owing to the difference of the pressure, a net force is produced to push the paper upward.

Experiment 2

When air is blown rapidly between the 2 ping pong balls, the 2 balls will move towards each other.

Explanation:
  1. Air move rapidly between the 2 balls, causes the pressure between the 2 balls to decrease.
  2. Pressure at the other side of the balls becomes relatively higher, push the 2 ball close to each other.

Experiment 3

The ping pong ball will not fall when water is allowed to flow through the filter funnel.

Explanation:
  1. Water above the ping pong ball flow rapidly, causes the pressure above the ping pong ball to decrease.
  2. As a result, the pressure below the ping pong ball is relatively higher.
  3. Owing to the difference of the pressure, a net force is produced to push the ping pong ball upward.

 

3.5.3 Appilcations of Archimedes Principle

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Plimsoll Line


The Plimsoll line is an imaginary line marking the level at which a ship or boat floats in the water.
It indicates how much load is allowed at different types of water.

Airship


  1. Air ship is filled with helium gas.
  2. Helium gas has density lower than the surrounding air, hence an upthrust which higher than the weight of the airship can be produced and cause the airship float in the air.

Hot Air Balloon


  1. Hot air in the balloon has lower density than the surrounding air.
  2. As a result, when the buoyant force produced is higher than the weight of the balloon, the balloon will start rising up.
  3. The altitude of the balloon can be controlled by varying the temperature of the air in the balloon.

Hydrometers


  1. Hydrometer is used to measure relative density of liquids.
  2. How deep the hydrometer sink into the liquid is affected by the density of the liquid.
  3. The lower the density of the liquid, the deeper the hydrometer will sink.
  4. This is used as the indicator of relative density of a liquid.

Submarine


A submarine use ballask tank to control its movement up and down.
To get submerge, water is pumped into the ballast tank to increase the weight of the submarine.
To surface, the water is pumped out to reduce the weight of the submarine.

Q & A

Q: The diagram shows a picture of a hydrometer. What is the function of the lead shot at the bottom of the hydrometer?

A: 

To lower down the centre of gravity of the hydrometer. The hydrometer will topple if the centre gravity of the hydrometer is above the surface of the liquid.

 

3.5.2 Principle of Floatation

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  1. The principle of floatation states that when an object floats in a liquid the buoyant force/upthrust that acts on the object is equal to the weight of the object.
  2. As shown in the figure above, if the weight of the object (W) = upthrust (F), the object is in balance and therefore float on the surface of the fluid.
  3. If the weight of the object > upthrust, the object will sink into the fluid.

Note

  1. Displaced volume of fluid = volume of the object that immerse in the fluid.
  2. If weight of the object > upthrust, the object will sink into the fluid.
  3. If weight of the object = upthrust, the object is in balance and therefore float on the surface of the fluid.

In order to solve the problem related to object immerse in water, it's important to know the all forces acted on the object.

Case 1:


  1. The density of the object is lower than the density of the liquid. The object floats on the surface of the water.
  2. The forces acting on the object is
    1. the weight of the object(W)
    2. the upthrust (F)
Forces are in equilibrium, hence

F = W

Case 2:

  1. The density of the object is greater than the density of the liquid. The object sink to the bottom of the water.
  2. Lying on the bottom of the water, there is a normal reaction acted on the object.
  3. The forces acting on the object is
    1. the weight of the object(W)
    2. the upthrust (F)
    3. Normal reaction (R)
Forces are in equilibrium, hence
F + R = W

Case 3:

  1. The density of the object is greater than the density of the liquid. The object is hold by a string so that it does not sink deeper into the water.
  2. The forces acting on the object is
    1. the weight of the object(W)
    2. the upthrust (F)
    3. Tension of the string (T)
Forces are in equilibrium, hence
F + T = W

Case 4:

  1. The density of the object is lower than the density of the liquid. The object is hold by a string so that it does not move up to the surface of the water.
  2. The forces acting on the object is
    1. the weight of the object(W)
    2. the upthrust (F)
    3. Tension of the string (T)
Forces are in equilibrium, hence

F = W + T

Example 1:



A metal block that has volume of 0.2 m³ is hanging in a water tank as shown in the figure to the left. What is the tension of the string? [ Density of the metal = 8 × 10³ kg/m³, density of water = 1 × 10³ kg/m³]

Answer:
Let,
Tension = T
Weight = W
Upthrust = F

Diagram below shows the 3 forces acted on the block.



The 3 forces are in equilibrium, hence



Example 2:
A wooden sphere of density 0.9 g/cm³ and mass 180 g, is anchored by a string to a lead weight at the bottom of a vessel containing water. If the wooden sphere is completely immersed in water, find the tension in the string.

Answer:
Let's draw the diagram that illustrate the situation:



We need to determine the volume of the displaced water to find the upthrust.
Let the volume of the wooden sphere = V


Let,
Tension = T
Weight = W
Upthrust = F

All the 3 forces are in equilibrium, hence


Example 3:



Figure above shows a copper block rest on the bottom of a vessel filled with water. Given that the volume of the block is 1000cm³. Find the normal reaction acted on the block.
[Density of water = 1000 kg/m³; Density of copper = 3100 kg/m³]

Answer:
Volume of the block, V = 1000cm³ = 0.001m³

Let,
Normal Reaction = R
Weight = W
Upthrust = F


Diagram below shows the 3 forces acted on the block.


All the 3 forces are in equilibrium, hence

 

3.5.1 Archimedes Principle

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  1. Archimedes Principle states that when a body is wholly or partially immersed in a fluid it experiences an upthrust equal to the weight of the fluid displaced.
  2. Upthrust/Buoyant force is an upward force exerted by a fluid on an object immersed in it.
  3. Mathematically, we write
F=ρVg
     F = Upthrust/Buoyant Force
     ρ = Density of the liquid
     V = Volume of the displaced liquid
     g = Gravitational field strength



Example 1:
Determine the upthrust acted on the objects immerse in the water below.
a.

b.

c.


Answer:
a. Upthrust = Weight of the displaced water = 15N

b. Upthrust = Weight of the displaced water = 32N

c. Upthrust = Weight of the displaced water = 20N


Example 2:
An iron block which has volume 0.3m³ is immersed in water. Find the upthrust exerted on the block by the water. [Density of water = 1000 kg/m³]

Answer:

Density of water, ρ = 1000 kg/m³
Volume of water, V = 0.3 m³
Gravitational Field Strength, g = 10 N/kg
Upthrust, F = ?


Example 3:

Figure above shows an empty boat floating at rest on water. Given that the mass of the boat is 150kg. Find
  1. the upthrust acting on the boat.
  2. The mass of the water displaced by the boat.
  3. The maximum mass that the boat can load safely if the volume of the boat at the safety level is 3.0 m³.

Answer:
a. According to the principle of flotation, the upthrust is equal to the weight of the boat.

Upthrust,
F = Weight of the boat
= mg = (150)(10) = 1500N

b. According to the Archimedes' Principle, the weight of the water displaced = Upthrust

Weight of the displaced water,
W = mg
(1500) = m(10)
m = 150kg

c.
Maximum weight can be sustained by the boat


Maximum weight of the load
= Maximum weight sustained - Weight of the boat
= 30,000 – 1,500 = 28,500N

Maximum mass of the load
= 28500/10 = 2850 kg


Example 4:

In figure above, a cylinder is immersed in water. If the height of the cylinder is 20cm, the density of the cylinder is 1200kg/m³ and the density of the liquid is 1000 kg/m³, find:
a. The weight of the object
b. The buoyant force

Answer:
a.
Volume of the cylinder, V  = 50 x 20 = 1000cm³ = 0.001m³
Density of the cylinder, ρ = 1200 kg/m³
Gravitational Field Strength, g = 10 N/kg
Weight of the cylinder, W = ?

b.
Volume of the displaced water = 50 x 12 = 600cm³ = 0.0006m³
Density of the water, ρ = 1000 kg/m³
Upthrust, F = ?
 


Example 5
The density and mass of a metal block are 5.0×103 kg m-3 and 4.0kg respectively. Find the upthrust that act on the metal block when it is fully immerse in water.
[ Density of water = 1000 kgm-3 ]

Answer:
In order to find the upthrust, we need to find the volume of the water displaced. Since the block is fully immersed in water, hence the volume of the water displaced = volume of the block.

Volume of the block,


Upthrust acted on the block,

 

3.4.3 Hydraulic Braking System and Hydraulic Jack

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Hydraulic Brake

In most vehicle, hydraulic system is used in the braking system, as shown in the figure below.


Usually, a disc brake is used in the front wheel of a car while a drum brake is used in the back wheel of a car.

Working Mechanism of Hydraulic Brake

  1. When the brake pedal is pressed, the piston of the master cylinder applies a pressure on the brake fluid.
  2. This pressure is transmitted uniformly to each cylinder at the wheel, cause the pistons at the wheels to push the brake shoes to press against the surface of the brake.
  3. The friction between the brakes and brake shoes causes the vehicle to slow down and stop.

Q & A

Q: Why is it dangerous if air bubble is trapped in the brake fluid of a braking system.

 A: 
  1. If air bubble is present in the fluid, the fluid become compressible. 
  2. This may prevent pressure transmits through the fluid and hence causing ineffective braking effect.

Q & A

Q: Why oil but not water is used as the hydraulic fluid in a hydraulic brake system?

 A:
  1. Because the boiling point of oil is much higher than water. This can prevent the hydraulic fluid from boiling when the brake is very hot. 
  2. Water may cause rusting in the part of the braking system

Hydraulic Jack

Working mechanism of a hydraulic jack.

  1. When the handle is pressed down, valve A is closed whereas valve B is opened. The hydraulic fluid is forced into the large cylinder and hence pushes the piston moving upward.

  3. When the handle is raised, valve B will be closed while vale A will be opened. Hydraulic fluid from the buffer tank will be suck into the small cylinder.

  5. This process is repeated until the load is sufficiently lifted up.
  6. The large piston can be lowered down by releasing the hydraulic fluid back to the buffer tank through the release vale.