PHYSICS As LEVEL(FORM FIVE) NOTES – HEAT-1

It can be easily seen through glass because it is opaque and shining liquid.
It does not wet glass no mercury remains on the sides of the glass tube when the mercury level falls.
It has low specific heat capacity. Therefore it does not absorb much heat from the body whose temperature is to be measured.

DISADVANTAGE OF USING MERCURY IN THE LIQUID IN GLASS THERMOMETERS

It cannot be used to measure very low as well as very high temperatures.

(ii) GAS THERMOMETERS

In most accurate work, temperatures are measured by gas thermometers.

There are two types of gas thermometers:

Constant volume gas thermometer
Constant pressure gas thermometer

JOLLY’S CONSTANT VOLUME GAS / AIR THERMOMETER

B1 is a glass bulb containing dry air

B2 is a glass tube containing mercury

B1 is connected to B2 by means of a capillary tube E bent twice at right angles

B3 is a glass tube containing mercury which is open the atmosphere at its upper end.

There is a fixed mark ―O‖ on the glass tube B2

The volume of air in B1 is maintained constant by raising or lowering the glass tube B3 until the mercury in B2 is at the fixed mark ―O‖.

OPERATION

When the thermometer is in use the bulb

is placed inside the enclosure whose temperature is required.

Keeping the volume of air in B1 constant by raising or lowering the glass tube B3, the pressure of air in B1 at ice point (0

), steam point (100

) and at the unknown temperature

) are determined.

If P denote pressure of a gas/air at constant volume, then one can talk of pressure at 0

100 and as P0, P100 and

respectively

Now, the unknown temperature

is given by:

Gas thermometer is an ideal thermometer because the increase in volume or pressure of a gas with temperature is independent of the nature of the gas.

All gases have the same coefficient of volume or pressure expansion.

ADVANTAGES OF USING GAS THERMOMETER

The gas thermometer has the following advantages:

It is more sensitive than liquid in glass thermometer because the expansion of gases is many times greater than that of any liquid.
The expansion of the gas is uniform and regular.
Gas scale temperatures degree with absolute scale of temperature.
It can be used to measure very low as well as very high temperatures.

Example

– Hydrogen gas thermometer can measure temperature from – 200

to 500

DISADVANTAGES OF USING GAS THERMOMETERS

The gas thermometer has the following disadvantages: –

Its use is inconvenient due to its very large size.
The air in the capillary tube is not at the temperature being measured.
It cannot be used to measure the temperature of a liquid available in small quantity.
It is not a direct reading thermometer. ie require skill

SOURCES OF ERRORS WHEN USING GAS THERMOMETERS

The bulb expands
Air is not an ideal gas

(iii)The air in the capillary tube is not at the temperature being measured

PLATINUM RESISTANCE THERMOMETER

The Platinum resistance thermometer is based on the principle that the electrical resistance of a pure metal increases with increasing in temperature and vice versa.

Experiments show that the resistance of a pure metal at any temperature

is given by:

Where R0 = Resistance at 0 , = Resistance at a temperature

It can be shown that where ‘a’ and ‘b’ are physical constant

In practice”b” is much less than ―a‖ and hence we can ignore the term b

= R0 (1 + a

)

Here ―a‖ is called temperature coefficient of resistance of the material of the wire (symbol,

)

For platinum wire

= 3.8 x 10-4/

-1

CONSTRUCTION

A sample from a platinum resistance thermometer consist of a platinum wire that would be around the mica former.

The wire is enclosed in a protective tube of quartz, glass or porcelain tube depending upon the type of application and temperature range.

The platinum wire is used because of its high temperature coefficient of resistance and high melting point (1773

)

Therefore, considerable change in resistance occurs for a relatively small change in temperature.

OPERATION

The platinum resistance thermometer forms one of the four arms of the Wheatstone bridge.

R1 and R2 are fixed resistors while R3 is a variable resistor.

The bridge is often kept at a considerable distance from the testing point

Under ordinary condition the bridge is balanced, that means the galvanometer shows no reading.

When the temperature changes the resistance r of the resistance thermometer also change

Consequently, the bridge no longer remains balance and some current flows through the galvanometer.

The change in resistance (and hence current through G) is a measure of the magnitude of temperature.

The accuracy of the platinum resistance thermometer depends on how accurately the bridge can be balanced.

Let R0, R100 and

be resistance of platinum wire at ice point (0

), steam point (100

) and at the unknown temperature

respectively

The temperature

of the scale is given by:

ADVANTAGES OF USING PLATINUM RESISTANCE THERMOMETER

High sensitivity (0.00005)
Small size
Measurements can be made over a wide range (260 – 1200)

DISADVANTAGES OF USING PLATINUM RESISTANCE THERMOMETER

High cost
Requires additional equipments such as the bridge circuit, power supply etc.
Larger size than thermocouple

(iv)THERMOCOUPLE THERMOMETER

A thermocouple is a device consisting of two dissimilar metal wires welded together at their ends.

A thermoelectric (

) is generated in the device when the ends are kept at two different temperatures.

The magnitude of the

generated is related to the temperature difference between the two junctions.

This enables a thermocouple to be used as a thermometer over a limited temperature range

OPERATION

One of the two junctions called the hot or measuring junction is placed at the temperature to be measured.

The other junction( the cold or reference junction) is maintained at a known reference temperature (usually 0

The

generated is measured by a suitable millvoltmeter or a potentiometer incorporated in the circuit.

The amount of the

generated depends upon the temperature difference between the hot and the cold junction

The greater the

the greater is the temperature difference between the junctions.

VARIATION OF THERMOELECTRIC

WITH TEMPERATURE

When the cold junction of a given thermocouple is kept constant at 0

and the hot is varied. The e. m. f is found to relate with the temperature

difference junction by the equation

Where A

B are constants.

This is a parabolic equation and hence a graph of E against

is a parabola of the nature shown in the figure below.

Where

Temperature of the cold junction

Neutral temperature

Inversion temperature

Neutral temperature (

)

Is the temperature at which the

of a thermocouple is maximum.

When the temperature is increased beyond the thermoelectric e. m. f decreases untill it becomes zero when the temperature is called inversion temperature.

Inversion Temperature

Is the temperature to which the hot junction of a thermocouple must be raised in order that the thermoelectric e. m. f in the whole circuit becomes zero.

THERMOCOUPLE

From the graph above

– =

+ =

2 = +

From the relationship between E and

Differentiating this equation with respect to

When

= 0 (slope of tangent at neutral temp)

0 = A + 2B

EXPRESSION OF INVERSION TEMPERATURE

From the relationship between E and

E = A – B 2

When E = 0 then =

When the inversion temperature is exceeded the thermoelectric (e. m. f) in the thermocouple is reversed.
The use of a thermocouple is restricted in the temperature range between 0 and neutral temperature It is because, beyond neutral temperature the thermoelectric e. m. f decreases with increasing temperature

ADVANTAGES OF USING THERMOCOUPLES

They have small heat capacities.

Therefore they have very little effect on the temperature of the body they are measuring.

They can measure rapidly fluctuating (changing) temperatures.

They are more accurate.

They are cheap and easy to use
They have a wide range of temperature measurement (-200 to 1500) depending upon the metals used.

DISADVANTAGES OF USING THERMOCOUPLES

Reference temperature has to be kept constant.
As the output voltage is less than 10mV a very sensitive meter is required. (iii) The variation of e.m.f with temperature is non-linear

(v) RADIATION THERMOMETERS (PYROMETERS)

For measuring very high temperatures radiation thermometers (Pyrometers) are used.

In these instruments high temperatures are measured by observing the radiation from the hot body.

The thermal radiation from the hot body is compared in terms of color with thermal radiation from the lamp filament.

When a pyrometer is used a hot wire filament in the pyrometer is viewed against a glowing object.

The filament current increased from zero until it makes the filament exactly the same color as the following object.

A meter in series with the filament can then be calibrated directly in terms of source temperatures, known using the laws of radiation.

They fall into two classes:

Total radiation py
rometer

Which respond to the total radiation from the hot body

Optical pyrometer

Which respond only to the visible light

Problem 01

A thermometer uses mercury as liquid in glass experiments show that the length of mercury at 0

and 100

are 5cm and 7cm respectively. At a certain temperature the length of the mercury is found to be 6.5cm, find this certain temperature. (Answer = 75 )

Problem 02

The pressure recorded by a constant volume gas thermometer at a Kelvin temperature T is 4.80 x 104Nm-2.

Calculate T if the pressure at triple point 273.16K is 4.20 x 104Nm-2. (Answer. T = 312K) Problem 03

The resistance of a platinum wire at a temperature

, measured on gas scale is given by

= R0 (1 + a + b 2)

Where

3.8 x 10-3 and

–5.6 x 10-7

What temperature will the platinum thermometer indicate when the temperature on a gas scale is 200

Problem 04

The pressure of air in a constant volume gas thermometer is 80cm and 109.3cm at 0

and

100

respectively. When the bulb is placed in hot water, the pressure is 100cm. calculate the temperature of hot water

Problem 05

The resistance of a platinum resistance thermometer is 100

at room temperature of 25

. In an experiment for measurement of temperature, the resistance of the thermometer is found to be 115.68

. find the value of temperature given that the temperature coefficient of resistance of platinum is 0.004/

Problem 06

A constant mass of a gas maintained at constant pressure has a volume of 200

at the temperature of melting ice, 273.2

at the temperature of water boiling under standard pressure and 525.1 at the normal boiling point of sulphur. A platinum wire has resistances of 2.00 , 2.778 , and 5.280

at these temperatures. Calculate the values of boiling- point of sulphur given by the two sets of observations and comment on the results.

Problem 07

In the thermocouple, the temperature of the cold junction is 10

while the neutral temperature is 270

. What is the value of temperature of inversion?.

Problem 08

In a certain thermocouple the thermo e. m. f E is given by

E =

Where

is the temperature of the hot junction and the cold junction being at 0

If = 10 V / and

= , find

The neutral temperature
The temperature of inversion

Problem 09

What does one require in order to establish a scale of temperature?
A Copper – constant thermocouple with its cold junction at 0 had an EMF of 4.28mV with its other junction at 100 . The EMF becomes 9.29mV when the temperature of the hot junction was 200 . If the EMF E is related to the temperature different by the equation E = A + B 2, Calculate

The values of A and B
The range of temperature of which E may be assumed proportional to without incurring an error of more that 1%?

Problem 10

The resistance

of a platinum varies with temperature t according to the equation

R0 (1 + 8000bt – bt2) where “b” is a constant.

Calculate the temperature on platinum scale corresponding to 400

on the gas scale

Problem 11

Define the thermodynamic temperature scale
The resistance of a platinum resistance thermometer is 1.20 when measuring a Kelvin temperature T of a body and 1.00 at the triple point of water. Find T and its centigrade equivalent.

Problem 12

What do you understand by the terms

Thermodynamic temperature scale
Triple point of water

The resistance of a platinum wire at temperature T measured on a gas scale is given by

R (T) = R0 (

)

What temperature will the platinum thermometer indicate when the temperature on the gas scale is 200

(Take

3.8 x 10-3 and

5.6 x 10-7)

Problem 13

Define

Thermodynamic temperature scale
How thermodynamic temperature donated and what is its SI unit?
Explain why a gas thermometer is seldom used for temperature measurement in the laboratory?

Study the table below and answer the questions which follow:

Calculate the temperature of the room for each thermometer
Explain why thermometers disagree in their values of room temperature.
What are the advantages of gas thermometer over liquid in-glass thermometers?

Problem 14

(a) (i) Describe how mercury in glass thermometer could be made sensitive.

(ii) A sensitive thermometer can be used to investigate the difference in temperature between the top and bottom of the waterfall. Calculate the temperature difference of the water fall 50m high.

(b) (i) Platinum resistance thermometer and constant volume gas thermometer are based on different thermometric properties but they are calibrated using the same fixed points. To what extent are the thermometers likely to agree when used to measure temperature near the ice point and near the steam point.

(ii)The resistance of the element of a platinum resistance thermometer is 2.0

at ice point and 2.73

at steam point. What temperature on the platinum resistance scale would correspond to resistance value of 8.34 and when measured on the gas scale the same temperature will correspond to a value of 1020 ? Explain the discrepancy.

Problem 15

(a). (i) What is meant by a thermometric property of a substance?

(ii) What qualities make a particular property suitable for use in practical thermometers

(b) Explain

Why at least two (2) fixed points are required to define a temperature scale?
Mention the type of thermometer which is most suitable for calibration of thermometers.

This is the transfer of heat energy from one body or system to another as a result of difference in temperature. In general heat energy transfers from the region of higher temperature to the region of lower temperature.

WAYS OF HEAT TRANSFER

There are three ways by which heat can be transferred

Conduction
Convection
Radiation

THERMAL CONDUCTION This is the process in which heat flows from the hot end to the cold end of the solid body without there being any net movement of the particles of the solid.

MECHANISM OF THERMAL CONDUCTION

MECHANISM 1

The molecules of a solid vibrate about their fixed positions with an energy that increases with temperature.

When a part of the solid is heated, the molecules there start vibrating more violently.

Since neighboring molecules are bound to each other, a molecule vibrating with larger energy will transfer some of its energy to its neighbors which in turn will transfer energy to the next neighbors and so on.

MECHANISM 2

In case of metals heat energy can also be transported by the free electrons.

Since the electrons are very small, they can travel rapidly around throughout the specimen transferring energy by collision to other electrons and other molecules.

Hence, the electrons are more effective in transferring energy from the hotter part to the colder part of the material than the mechanism explained above (mechanism 1)

This explains why thermal conduction in metals is much more than that in insulators

In metals heat energy is mainly carried by the free electrons although some energy is carried by intermolecular vibration.

IMPORTANT TERMS

RATE OF HEAT FLOW

Symbol,

This is the heat flow per unit time in a material

TEMPERATURE DIFFERENCE

Symbol ( – ) or d

This is the difference between higher and lower temperatures.

Heat flows from the region of higher temperature to the region of lower temperature and if

> then,

Temperature difference =

–

TEMPERATURE GRADIENT

Symbol

This is the temperature difference per unit length of the material.

It is a fall of temperature with distance between the ends of the body in the direction of heat flow.

Temperature gradient =

STEADY CONDITION

This is an equilibrium point in a material when at every point the temperatures are constant.

LAGGED MATERIAL

A material enclosed by an insulator (bad conductor of heat) so that the heat loss to the surrounding is negligible.

UNLAGGED MATERIAL

A material which is not enclosed by an insulator so that the heat is lost to the surrounding.

TEMPERATURE DISTRIBUTION ALONG THE CONDUCTOR

1. UNLAGGED CONDUCTOR

Consider an unlagged metal bar AB whose ends have been soldered into the metal tanks H and C

H contains boiling water and C contains ice water.

Heat flows from the hot end to the cold end of the bar and when the conditions are steady the temperature

are measured at points along the length of the bar.

This happens simply because some amount of heat is lost to the surrounding by convection and radiation.

2. LAGGED CONDUCTOR

If the metal bar is well-lagged with a bad conductor of heat such as asbestos and wool the temperature now falls uniformly from the hot end to the cold end of the bar.

A graph of temperature against length of the bar is shown below:

Since the metal bar is well-lagged no heat is lost to the surrounding and a graph of fall of temperature against length of the bar is a straight line (see figure above)

THERMAL CONDUCTIVITY

It is measure of the ability of a material to conduct heat.

Consider a conductor of length L of cross – sectional area A

Let and be temperature on the opposite sides of the conductor with

Experiments show that the heat flow per second

from the hot sides to the cold side of the conductor is:

Directly proportional to the cross-sectional area A of the conductor

Directly proportional to the temperature difference – ) between the two sides

– )

Inversely proportional to the perpendicular distance between the concerned faces

Combining the above three factors:

Where K = constant of proportionality called coefficient of thermal conductivity (thermal conductivity) of the material.

Equation (1) above assumes that:

The opposite sides are parallel
There is no heat loss through the sides.

From equation (1)

Definition

The coefficient of thermal conductivity K of a material is the rate of flow of heat per unit area per unit temperature gradient when the heat flow is perpendicular to the faces of a thin parallel – sided slab of the material under steady state conditions.

UNIT OF K

From equation (2)

K =