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

1. Length of liquid column in a glass tube
2. Volume of a gas at constant pressure
3. Pressure of a gas at constant volume
4. Electrical resistance of a platinum wire
5. Electromotive force of a thermo-couple

1. A marked degree of expansion for a small temperature rise
2. A uniform expansion rate
3. Good thermo conductivity
4. High boiling point and low freezing point (if it is liquid)

1. CELSIUS SCALE

This is a temperature scale in which the fixed points are the temperatures at standard pressure of ice in equilibrium with water (0) and water in equilibrium with steam (100)

The temperature on this scale is expressed in degree Celsius ()

2. FAHRENHEIT SCALE

This is a temperature Scale in which the temperature of boiling water is taken as 212 and the temperature of pure melting ice is taken as 32

The interval between these two reference temperatures is divided into 180 equal parts and each part is called degree Fahrenheit ()

To convert this scale into degree centigrade (), the formula is:

3. THERMODYNAMIC TEMPERATURE SCALE

Thermodynamic temperature is also called absolute temperature. The degree centigrade is equal in magnitude to temperature in Kelvin i.e a change of temperature in is equal to a change of temperature in Kelvin.

1. The length of liquid column in a glass tube varies linearly and continuously with temperature.

Length temperature

= k + 0

Compare y = +

2. The volume of a gas at constant
   pressure varies linearly and continuously with temperature.

Volume temperature

V T

• V = K T + 0

Compare y = +

3. The pressure of a gas at constant volume varies linearly and continuously with temperature

Pressure temperature

P T

• P = K T + 0

Compare y = +

1. Ice point

2. Steam Point

3. Triple point

Let X0 be physical property of a material at ice point (0)

Temperature	Physical Property
0	X0
100	X100

When the temperature changes from 0 to 100

Change in temperature = 100 – 0

= 100

Change in property = –

But change in temperature change in thermometric property

100 ( – )

100 = K( – ) …………………………….(1)

When the temperature changes from 0

Change in temperature =

=

Change of the thermometric property = –

But change in temperature change in thermometric property

– )

= ……………………………..(2)

Dividing

=

Since change in temperature change in thermometric property we have

T Trip P Trip

T Trip = k P Trip ………………………………….(1)

Similarly T PT

T = kPT…………………………….(2)

Dividing

=

T = x T Trip

2. Gas thermometers
3. Platinum resistance thermometers
4. Thermocouple thermometers
5. Radiation thermometers (Pyrometers)

This means that in the temperature scale equation, becomes length

The temperature of the thermometer in terms of length of mercury is given by:

When, = length of mercury at ice point

length of mercury at steam point

Length of mercury at the unknown temperature

1. Its boiling point 357 and its freezing point is – 36

2. Its expansion is nearly uniform over the ordinary range of temperatures.

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

1. Constant volume gas thermometer
2. Constant pressure gas thermometer

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:

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

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

– Hydrogen gas thermometer can measure temperature from – 200 to 500

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

1. The bulb expands
2. Air is not an ideal gas

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 b2

= R0 (1 + a)

)

For platinum wire = 3.8 x 10-4/-1

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

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:

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

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

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.

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

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.

THERMOCOUPLE

– =

+ =

2 = +

From the relationship between E and

E

Differentiating this equation with respect to

When = 0 (slope of tangent at neutral temp)

0 = A + 2Bn

2B

From the relationship between E and

E = A – B 2

When E = 0 then =

1. When the inversion temperature is exceeded the thermoelectric (e. m. f) in the thermocouple is reversed.
2. 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

1. They have small heat capacities.

2. They can measure rapidly fluctuating (changing) temperatures.

3. They are more accurate.

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

1. Reference temperature has to be kept constant.
2. 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

1. Total radiation py
   rometer

2. Optical pyrometer

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 )

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

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

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/.

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.

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?.

E = +

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

If = 10 V / and = , find

1. The neutral temperature
2. The temperature of inversion

1. What does one require in order to establish a scale of temperature?
2. 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

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

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

1. Define the thermodynamic temperature scale
2. 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.

1. What do you understand by the terms

1. Thermodynamic temperature scale
2. Triple point of water

2. 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)

1. Define

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

2. Study the table below and answer the questions which follow:

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

(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.

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

1. Conduction
2. Convection
3. Radiation

1. RATE OF HEAT FLOW

Symbol,

2. TEMPERATURE DIFFERENCE

Symbol ( – ) or d

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

Temperature difference = –

3. TEMPERATURE GRADIENT

Symbol or

Temperature gradient = =

4. STEADY CONDITION

5. LAGGED MATERIAL

6. UNLAGGED MATERIAL

1. UNLAGGED CONDUCTOR

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.

2. LAGGED CONDUCTOR

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:

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

A

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

– )

3. Inversely proportional to the perpendicular distance between the concerned faces

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

Definition

K =

=

=

……………………..(3)

Where = Temperature gradient

The sign show that the heat flows in the direction of decreasing temperature i.e the temperature diminishes as the length increases. The value of K for some common substances at room temperature are as shown in the table below:

Substance for which is small is bad conductors of heat.

The rate at which heat flows is one material is equal to that in the other material.

= K1A = K2A

Where , and are the temperatures at the ends of the bars respectively.

= KA

I =

From equation (1) and equation (2) above both and I are flow quantities.

In equation (1) the heat flows per second produced by a temperature difference.

Thus, the quantity is thermal Equivalent of

=

Where = conductor length

=

But =