yogendra

Heat is defined as energy in transit.

The temperature of a system can be defined as the property that determines whether or not the body is in thermal equilibrium with the neighboring systems. If a number of systems are in thermal equilibrium, a single numerical vale called the temperature can represent this common property of the system. It means that if two systems are not in thermal equilibrium, they are at different temperatures.

Thermometry

The branch of heat relating to the measurement of temperature (degree of hotness) of a body is called thermometry. Thermometer is the instrument used to measure the temperature of a body.

Types of Thermometers. There are different kinds of thermometers

(i) Liquid thermometers. These thermometers are based on the principle of change in volume of a liquid with change in temperature. Mercury and alcohol thermometers are based on this principle.

(ii) Gas thermometers These are based on the principle of change in pressure or volume with change in temperature, Eg: Callendar's constant pressure thermometer, constant volume hydrogen thermometer, etc.

(iii) Resistance thermometers. These are based on the principle of change in resistance with change in temperature, Eg: platinum resistance thermometer.

(iv) Thermo-electric thermometers: These are based on the principle of thermo-electricity, Eg :- production of thermo -EME in a thermo-couple when the two junctions are at different temperatures.

(v) Radiation thermometers: These are based on the quantity of heat radiations emitted by a body Ex: -furnaces. These instruments are known as pyrometers.

(vi) Vapour pressure thermometers: These are based on the principle of change of vapour pressure with change in temperature. These are used to measure low temperatures, Ex:- helium vapour pressure thermometer, etc.

Celsius. Fahrenheit and Reaumur Relation:

C = F -32 = R
100 180 80

Relation between Celsius. Kelvin. Fahrenheit and Rankin Relation:

C -0 = F -32 = K -273 = R
100 180 100 80


Specific Heat

When a body is heated, its temperature rises. If 100gm of copper and 100gm of water are heated by similar burners for the same time, the rise in temperature is not the same in the two cases. The rise in temperature depends on the quantity of heat given to the body and the nature of its material. Let Q be the quantity of heat given to a body of mass m and let the rise in temperature be e. Then, Q = mse

Where s is a constant that depends upon the nature of the substance. S is called the specific heat of the substance.

Calorie It is the quantity of heat required to raise the temperature of one gram of water from 14.5° to15.5° C. This is the standard unit recommend by International Committee of Pure Physics.

For ordinary purposes, the specific heat of water is taken as 1, but specific heat of water is not 1 at all temperatures. For practical purposes calorie may be defined as the amount of heat required to raise the temperature of 1 gm of water through 1° C.

Kilogram Calorie It is the amount of heat required to raise the temperature 1 kg of water through 10 c.
1 kg calorie = 1000 calories.

British Thermal Unit It is the amount of heat required to raise the temperature of 1 pound of water through 10F. 1 BTU = 252 calories.

Therm It is the amount of heat required to raise the temperature of 105 pounds of water through 10F.
1 Therm = 2.52 x 107 calories.

Pound Calorie It is the amount of heat required to raise the temperature of 1 pound of water through 10c.
1 pound calories = 453.6 calories.
UNITS OF HEAT



Unit
Quantity of water
Rise in temp
Relation

Calorie
1gm
10c
= 1 calorie
Kg Calorie
1kg
10c
= 1000 calories
BTU
1 pound
10 F
= 252 calories
Therm
105pound
10 F
= 2.52 x 107 calories
Pound Calorie
1 pound
10c
= 453.6 Calories


Specific Heat Specific heat is defined as the quantity of heat required to raise the temperature of one gram of a substance through 10c. The specific heat of a substance is not constant and it is different at different temperatures. Ordinarily, the specific heat determined is the mean specific heat, Suppose, m is the mass of the substance, s is the mean specific heat and if Q units of heat is required to raise its temperature from q1 to q2 , then the mean specific heat
s = Q / m(q2 - q1)

For qualitative work, if dQ heat is given to raise the temperature of m grams of substance through dq.
dQ = m s dq
s = 1 x dq
m x dt

The unit of specific heat is ‘cal/g0 c

Thermal Capacity It is the quantity of heat required to raise the temperature of the whole of the substance through 10C. Let the mass of the substance be m and its specific heat s

Thermal capacity = m x S x 1
= ms calories.
Water Equivalent It is the amount of water that will absorb the same quantity of heat as the substance for the same rise in temperature. Let the mass of the substance be m, specific heat s and rise in temperature q.
Q = mse
If the water equivalent = W
Q = W x 1 x q
W x 1 x q = mse (OR) W = ms grams
Water equivalent is numerically equal to the thermal capacity but the unit of water equivalent is gram and that of thermal capacity is calorie.

Change of State

A substance can exit three states viz. Solid, Liquid and Gas. The particular state of a substance depends on its temperature. According to the kinetic theory, the molecules of a substance in the solid state have less degree of freedom than a substance in the liquid or gaseous state. The molecules are more free to move in the gaseous state. The change in state can be brought about by supplying or withdrawing heat from the substance. Ice is the solid state of water. By supplying heat to ice, it can be changed into water. Similarly by supplying heat to water, it can be converted into the gaseous state (steam). This is true for all substances. Even permanent gases like oxygen, nitrogen, hydrogen etc can be liquefied at low temperatures.

For a given substance the change of state takes place at a fixed temperature and pressure. When the substance changes from the solid to the liquid state, the heat supplied at the constant temperature (called melting point) is used to overcoming the forces of intermolecular attraction. The mean molecular distance increases and the molecules from the liquid to the gaseous state at a fixed temperature (called the boiling point) and pressure. The heat supplied is used in increasing the mean molecular distance. The molecules become free to move about in the whole space available to them.

Latent Heat of Fusion

Take small pieces of ice in a beaker. Fix a thermometer to note the temperature of ice in the beaker. Heat the beaker slowly. Ice melts but the thermometer does not show any rise in temperature. When the whole of ice has melted the temperature of water rises and the thermometer indicates it. During the process of conversion from ice to water (change of state from solid to liquid) the heat supplied is used to change the state of ice from solid state to liquid state. This heat is called latent heat. Latent means hidden i.e.. Which is not indicated by the thermometer.

It has been found that one-gram of ice takes 80 calories of heat to get it converted to water. This heat is called latent heat of fusion of ice. Its unit is 'cal/gram'.

Latent heat of a substance is defined as the amount of heat required change the state of one gram of substance from solid to liquid without any change in its temperature.

Law of Fusion

(1) Every substance changes its state from solid to liquid at a particular temperature (under normal pressure) called the melting point.

(2) As long as the change of state takes place there is no change in temperature.

(3) One gram of every substance requires a definite quantity of heat for change of state from solid to liquid and it is called the latent heat of fusion of that substance. It is different for different substance.

(4) Some substances show increase in volume on melting e.g., wax, ghee, etc. While some other substances show decrease in volume on malting e.g., ice
(5) The melting point of those substance which decrease in volume on melting, is lowered with increase in pressure.

(6) The melting point of those substance which increase in volume on melting, is increased with increases in pressure.

Note
(1) Ice decreases in volume on melting and its melting point is lowered with increases in pressure.
(2) The melting point or solidification point is the same for a substance.
Laws of Boiling
(1) Every liquid changes its state from liquid to its vapour at a particular temperature (under normal pressure) called the boiling point.

(2) As long as the change of state takes place, there is no change in temperature.

(3) One gram of every liquid requires definite quantity of heat for change of state from liquid to vapour and it is called the latent heat of vaporization of that liquid. Latent heat is different for different substances.
(4) All liquids show increase in volume on vaporization.
(5) The boiling point of a liquid increase with increase in pressure of a liquid.
(6) The liquid can boil at a lower temperature under reduced pressure.

Latent Heat of Vaporization

The latent heat of vaporization of a liquid is the amount of heat required to convert one gram of the liquid into vapour without any change in temperature. For water, latent heat of vaporization is 537 cals/grm at a pressure of 75cm of Hg. Latent heat of vaporization is different for different substances.

Conduction Is the process in which heat is transmitted from one point to the other through the substance without the actual motion of the particles? When one end of a metal bar is heated, the molecules at the hot end vibrate with higher amplitude (kinetic energy) and transmit that heat energy from one particle to the next and so on. However the particles remain in their mean positions of equilibrium. (This process of conduction is prominent in the case of solids. The property of transmission of heat has been used in Davy's safety lamp. Materials having less conductivity e.g. granite, brick walls boiler etc. The space between the two walls of a thermos flask is evacuated because vacuum is a poor conductor of heat. The air enclosed in the woolen fabric helps in protecting us from cold because air is a poor conductor of heat.

Convection is the process in which heat is transmitted from one place to the other by the actual movement of the heated particles. It is prominent in the case of liquids and gases. Land and sea breezes, and trade winds are formed due to convection. Convection plays an important part in ventilation; gas filled electric lamps and heating of buildings by hot water
circulation.

Radiation is the process in which heat is transmitted from one place to the other directly without the necessity of the intervening medium. We get heat radiations directly from the sun without affecting the intervening medium. Heat radiation's can pass through vacuum. Their properties are similar to light radiations.

Examples

1. Find the value of absolute zero of the Fahrenheit scale.
F –32 = A –273
180 100
Here A = 0
F = -180 x 273 + 32
100
= -456.40F

2. There is a certain temperature which has the same reading on both centigrade and Fahrenheit thermometers. Find the temperature.

F -32 = A -273
180 100
Here F = C = x
\ x – 32 = x
180 100
(OR)

x –32 = 9/5x
\ x = -40
\-400C = -40 0F

3. A faulty thermometer has its fixed points marked 5 and 95. What is the correct temperature in centigrade when this thermometer records 59?
Let the reading on the centigrade thermometer be °c

C = R-L.F.P.
100 P.-L.F.P.
\ c = 59-5
100 95-5
c = 54
100 90

C = 600C

4. A certain mass of gas exerts a pressure of 72 cm of mercury at 2~C. It is heated at constant volume and the pressure observed after some time is 90cm of mercury. Calculate the temperature.

Here P1 = 72 cm of Hg P2 = 90cm of Hg
V1 = V V2 = V
T1 = 273 + 27 = 3000 A0 T 2 = ?

P2 v2 = p1 v1 (OR) 90v = 72v
T2 T1 T2 300

T2 = 90 x 300 = 3750A = 020c
72
5. Calculate how much steam from water boiling at 100 0C will just m 200gm of wax at 15°C. (Melting point of wax = 550C, S.P. Latent heat of fusion of x = 35 cal/gm)

Suppose mass of steam = m
Mass of wax = 200gm
Sp. Heat of wax = 0.7
Latent heat of wax = 35 cal/gm
Initial temperature of wax = 150C
Melting point of wax = 550C
Heat required to rise the temperature of wax from 150C to550C
= 200 x 0.7 x (55 -15) = 5600 cal
Heat required to melt wax at 550C = 200 x 35 = 7000 cal
Total heat gained by wax = 5600 + 7000 = 12,600 cal

Heat lost by steam = m x 540 + m (100- 55)
= 540m + 45m = 585m
Heat lost = Heat gained
585m = 12,600
m = 21.54gm

6. How much ice at 00C would a kilogram of steam at 1000C melts, if the resulting water is at 00C ? Latent heat of ice = 80cal/gm and latent heat of steam = 536 cal/gm.

Mass of ice = M gm
Mass of steam = 1 kg = 1000 gm
Temper of stem = 1000 C
Final temp = 00C
Heat gained by ice = M x 80 cal
Heat lost by ice steam = 1000 x 536 + 1000 x 100
= 636000cal
Heat gained = Heat lost
80 M = 636000
M = 7950 gm
= 7.95kg

7. A piece of metal weighing 60 gm at 100C was immersed in a current of steam 1000C . Calculate the amount of steam condensed. Specific heat of the metal is 0.1 cal/gm - 0C and latent heat of steam is 540 cal/gm.

M = 60gm
S = 0.1 cal/gm - 0C
T1 = 100C
T2 = 100°C

Heat taken by the metal = MS(T 1 -T 2)
= 60 x 0.1 (100 -10)
= 540 cal.
Suppose the mass of steam condensed = m grams
Latent heat of steam,
L = 540cal/gm .
\Heat lost by steam,
m L = m x 540
Heat gained = Heat lost
540 = 540m
\m = 1 gm
(OR) Hence, the mass of steam condensed = 1 gram.

8. An electric heater rod is dipped in a vessel containing water at 00C. The electric rod produces heat at the rate of 3000J/s. The vessel with its contents is maintained at 00 C by adding ice at the rate of 9 g/s. Calculate the specific latent heat of fusion of ice. If the total heat capacity of the water, the vessel and its contents is 12000j/K, at what rate does the temperature start rising when the supply of ice is stopped.


(1) Here H = 3000J/s
m = 9 g/s = 9 x 10-3 kg/ s
H = mL
L = H/m
L = 3000
9 X 10 -3
L = 3.33 x105 J/Kg.

(2) When the supply of ice is stopped, let the rate of rise of temperature be q k/s
w = 12000J/Kg
H = 3000 J/s
H = Wq
q = H/W
q = 3000
12000
q = 0. 25Kg/s.

9. lt is found that 65,45,000 cal of heat are transmitted per minute across a sheet of silver 10cm square and 1 mm thick, with a difference of temperature between its faces 1100C. Find the coefficient of thermal conductivity of silver.

Q = 65,45,000 cal, time t=1 min = 60sec
Each side of the square = 10cm
\Area of cross-section
A = 1 mm = 1/10cm, q1 -q2 = 1100C
Q = kA(q1 -q2 ) t
D
(OR)
K = Q x d = 65,45,000 x 1
A (q1 -q2)t 10 x 100 x 110 x 60
= 0.99

10. Estimate the rate at which ice would melt in a wooden box 2cm thick and of inside measurements 100 x 60 x 60 cm. Assuming that the external temperature, is 30oC and K for wood = 0.0004.

Thickness of the box = d = 2cm
q1 = 300c
q2 = 00c
(q1-q2) = 300c
Surface area of the box
A = 2 x 100 x 60 + 2 x 60 x 60 + 2 x 100 x 60
= 31200 sq cm
Q = kA(q1 -q2 ) t
D
= 0.0004 x 31200 x 30 x 1
2
= 187.2 cal


Suppose the amount of ice melted = m grams
Q = 80 m
M = 2.34 grams

11. The height of Niagra falls is 50 meters. Calculate the difference between the temperature of water at the top and the bottom of the falls. (J=4.2 x 107 ergs/cal) h = 50meters = 5000 ergs

suppose difference of temperature = o C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x e calories W = JH

suppose difference of temperature = u C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x q calories
W = JH
M x 980 x 5 000 = 4.2x107 x m x q
q = 980 x 5000
42 x107

12. A 12kg mass falls through 23mm on to the ground and bounces to a height of 0.50.? Assuming that all the potential energy to is used in heating up the mass, 'calculate the temperature rise. Take specific heat capacity of the material as 600 joules/kg0C and the force of gravity on 1kg = 10 Newton.

M = 12kg
S = 600joules/kg -0C
h1 = 23mm
q = ?
h2 = 0.50 mm
g = 10 m/s2 (given)
Loss in potential energy = Mg (h1 – h2)
= 12 x 10(23- 0.50)
= 2700joules
= Msq
= 2700joules
\q = 2700 = 0. 375 0C.
12x600

Eg.13. Convert 50°C into Farenheit and 68°F into Centigrade. (HMT -1995)

Eg.14. Why is better to wear dark clothes in winter and bright clothes in summer. (HMT -1995)

Eg.15.A man has a temperature of 99.8° F what will be the thermometer shows if it measures temperature in degrees Celsius? (HMT-1994)

Eg.16. A measuring unit of power

Eg.17. The velocity of light is
(a) 313 m/sec (b) 330 m/s (c) 303 m/s (d). none Of these