Thermodynamics Class 11 Notes Physics Chapter 11

 Page 1


Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND 
CALORIEMETRY
8.1 Heat
The	 ener gy 	 associated 	 with 	 configuration 	 and 	 random 	 motion 	 of 	 the 	 atoms 	
and	 molecules 	with 	in 	a 	body	is 	called 	heat.
(1)	 Units 	: 	Joule 	(S.I.) 	and 	calorie 	(Practical 	unit)
(2)	 The 	ratio 	 of 	work	done 	(W) 	to 	heat 	produced 	(Q) 	 is 	constant.
J 	is 	called 	mechanical 	equivalent	of 	heat 	and 	has 	v alue 	4.2	J/cal. 	
1	calorie	 = 	4.186	Joule 	= 	4.12	Joule
(3)	 Heat 	 is 	 a 	 path 	 dependent 	 and 	 is 	 taken 	 to 	 be 	 positive 	 if 	 the 	 system 	 absorbs 	
it 	and 	negative 	if 	releases 	it.
8.2 Temperature
T emperature 	 is 	 defined 	 as 	 the 	 degree 	 of 	 hotness 	 or 	 coldness 	 of 	 a 	 body .	 Heat 	
flows 	from 	higher 	temperature 	to 	lower 	temperature.
T wo 	bodies 	are 	said 	to 	be 	in 	thermal 	equilibrium 	when 	both 	the 	bodies 	are 	
at	the 	same 	temperature. 	 T emperature 	a 	kinetic 	ener gy 	
8.3 Scales of Temperature
The 	 K elvin 	 temperature 	 s cale 	 is 	 als o 	 know n 	 as 	 thermodynamic 	 s cale. 	 The 	 S .I.	
unit 	 of 	 temper ature 	 is 	 kelvi n 	 and 	 is 	 defined 	 as 	 (1/273.16) 	 of 	 the 	 temperature	
of	 the 	 triple 	 point 	 of 	 water . 	 The	 triple	 point 	 of 	 water 	 is 	 that 	 point 	 on	 a 	 P–T 	
diagram 	 where 	 the 	 three 	 phases 	 of 	 water , 	 the 	 solid, 	 the 	 liquid 	 and 	 the 	 gas, 	
Page 2


Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND 
CALORIEMETRY
8.1 Heat
The	 ener gy 	 associated 	 with 	 configuration 	 and 	 random 	 motion 	 of 	 the 	 atoms 	
and	 molecules 	with 	in 	a 	body	is 	called 	heat.
(1)	 Units 	: 	Joule 	(S.I.) 	and 	calorie 	(Practical 	unit)
(2)	 The 	ratio 	 of 	work	done 	(W) 	to 	heat 	produced 	(Q) 	 is 	constant.
J 	is 	called 	mechanical 	equivalent	of 	heat 	and 	has 	v alue 	4.2	J/cal. 	
1	calorie	 = 	4.186	Joule 	= 	4.12	Joule
(3)	 Heat 	 is 	 a 	 path 	 dependent 	 and 	 is 	 taken 	 to 	 be 	 positive 	 if 	 the 	 system 	 absorbs 	
it 	and 	negative 	if 	releases 	it.
8.2 Temperature
T emperature 	 is 	 defined 	 as 	 the 	 degree 	 of 	 hotness 	 or 	 coldness 	 of 	 a 	 body .	 Heat 	
flows 	from 	higher 	temperature 	to 	lower 	temperature.
T wo 	bodies 	are 	said 	to 	be 	in 	thermal 	equilibrium 	when 	both 	the 	bodies 	are 	
at	the 	same 	temperature. 	 T emperature 	a 	kinetic 	ener gy 	
8.3 Scales of Temperature
The 	 K elvin 	 temperature 	 s cale 	 is 	 als o 	 know n 	 as 	 thermodynamic 	 s cale. 	 The 	 S .I.	
unit 	 of 	 temper ature 	 is 	 kelvi n 	 and 	 is 	 defined 	 as 	 (1/273.16) 	 of 	 the 	 temperature	
of	 the 	 triple 	 point 	 of 	 water . 	 The	 triple	 point 	 of 	 water 	 is 	 that 	 point 	 on	 a 	 P–T 	
diagram 	 where 	 the 	 three 	 phases 	 of 	 water , 	 the 	 solid, 	 the 	 liquid 	 and 	 the 	 gas, 	
can	 coexist 	in 	thermal 	equilibrium.
T o 	 construct 	 a 	 scale 	 of 	 temperature, 	 two	 fixed	 points 	 are 	 taken. 	 First 	 is 	 the 	
freezing 	 point 	 of 	 water ,	 it 	 is 	 called 	 lower 	 fixed 	 point.	 The 	 second 	 is 	 the 	 boiling	
point 	of 	water ,	it 	is 	calle d 	upper 	fixed	point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius	 ºC	 0ºC	 100ºC	 100
Fahrenheit	 ºF	 32ºF	 212ºF	 180
Reaumer	 ºR	 0ºR	 80ºR	 80
Rankine	 ºRa	 460 	Ra	 672 	Ra	 212
Kelvin	 K	 273.15 	K	 373.15 	K	 100
T emperature 	 on	 one 	 scale 	 can 	 be 	 converted 	 into 	 other 	 scale 	 by	 using 	 the 	
following 	identity .
	=	Constant 	for 	all	scales
8.4 Thermal Expansion
When 	matter 	is 	heated, 	it 	expands.
(i)	 Coefficient 	of 	linear 	expansion 	a 	= 	
(ii)	 Coefficient 	of 	superficial 	expansion 	 ß 	= 	
(iii)	 Coefficient 	of 	volume 	expansion 	 ? 	= 	
(iv)	 The 	 value 	 of 	a, ß and ? 	 depends 	 upon	 the 	 nature 	 of 	 material. 	 All 	 have 	 
dimension 	[?
–1
] a nd 	unit 	per 	ºC.
(v)	 ? L 	= 	La?T,	?A 	=	Aß?T and ?V 	=	 V??T
(vi)	 Final 	length	 L ’ 	 =	 L 	+ 	? L 	= 	L 	(1 	+ 	a?T)
Final 	area 	 A ’ 	 =	 A 	+ 	? A 	= 	 A 	(1 	+ 	ß?T)
Page 3


Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND 
CALORIEMETRY
8.1 Heat
The	 ener gy 	 associated 	 with 	 configuration 	 and 	 random 	 motion 	 of 	 the 	 atoms 	
and	 molecules 	with 	in 	a 	body	is 	called 	heat.
(1)	 Units 	: 	Joule 	(S.I.) 	and 	calorie 	(Practical 	unit)
(2)	 The 	ratio 	 of 	work	done 	(W) 	to 	heat 	produced 	(Q) 	 is 	constant.
J 	is 	called 	mechanical 	equivalent	of 	heat 	and 	has 	v alue 	4.2	J/cal. 	
1	calorie	 = 	4.186	Joule 	= 	4.12	Joule
(3)	 Heat 	 is 	 a 	 path 	 dependent 	 and 	 is 	 taken 	 to 	 be 	 positive 	 if 	 the 	 system 	 absorbs 	
it 	and 	negative 	if 	releases 	it.
8.2 Temperature
T emperature 	 is 	 defined 	 as 	 the 	 degree 	 of 	 hotness 	 or 	 coldness 	 of 	 a 	 body .	 Heat 	
flows 	from 	higher 	temperature 	to 	lower 	temperature.
T wo 	bodies 	are 	said 	to 	be 	in 	thermal 	equilibrium 	when 	both 	the 	bodies 	are 	
at	the 	same 	temperature. 	 T emperature 	a 	kinetic 	ener gy 	
8.3 Scales of Temperature
The 	 K elvin 	 temperature 	 s cale 	 is 	 als o 	 know n 	 as 	 thermodynamic 	 s cale. 	 The 	 S .I.	
unit 	 of 	 temper ature 	 is 	 kelvi n 	 and 	 is 	 defined 	 as 	 (1/273.16) 	 of 	 the 	 temperature	
of	 the 	 triple 	 point 	 of 	 water . 	 The	 triple	 point 	 of 	 water 	 is 	 that 	 point 	 on	 a 	 P–T 	
diagram 	 where 	 the 	 three 	 phases 	 of 	 water , 	 the 	 solid, 	 the 	 liquid 	 and 	 the 	 gas, 	
can	 coexist 	in 	thermal 	equilibrium.
T o 	 construct 	 a 	 scale 	 of 	 temperature, 	 two	 fixed	 points 	 are 	 taken. 	 First 	 is 	 the 	
freezing 	 point 	 of 	 water ,	 it 	 is 	 called 	 lower 	 fixed 	 point.	 The 	 second 	 is 	 the 	 boiling	
point 	of 	water ,	it 	is 	calle d 	upper 	fixed	point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius	 ºC	 0ºC	 100ºC	 100
Fahrenheit	 ºF	 32ºF	 212ºF	 180
Reaumer	 ºR	 0ºR	 80ºR	 80
Rankine	 ºRa	 460 	Ra	 672 	Ra	 212
Kelvin	 K	 273.15 	K	 373.15 	K	 100
T emperature 	 on	 one 	 scale 	 can 	 be 	 converted 	 into 	 other 	 scale 	 by	 using 	 the 	
following 	identity .
	=	Constant 	for 	all	scales
8.4 Thermal Expansion
When 	matter 	is 	heated, 	it 	expands.
(i)	 Coefficient 	of 	linear 	expansion 	a 	= 	
(ii)	 Coefficient 	of 	superficial 	expansion 	 ß 	= 	
(iii)	 Coefficient 	of 	volume 	expansion 	 ? 	= 	
(iv)	 The 	 value 	 of 	a, ß and ? 	 depends 	 upon	 the 	 nature 	 of 	 material. 	 All 	 have 	 
dimension 	[?
–1
] a nd 	unit 	per 	ºC.
(v)	 ? L 	= 	La?T,	?A 	=	Aß?T and ?V 	=	 V??T
(vi)	 Final 	length	 L ’ 	 =	 L 	+ 	? L 	= 	L 	(1 	+ 	a?T)
Final 	area 	 A ’ 	 =	 A 	+ 	? A 	= 	 A 	(1 	+ 	ß?T)
Final 	volu me	 V’ 	 =	 V 	+ 	? V 	= 	 V 	(1 	+ 	??T)
(vii) 	ß 	= 	2	a and ? = 	3	a
8.5 Anomalous Expansion of Water
(1)	 In 	case 	 of 	 water , 	 it 	 expands 	 on	 heating 	 if 	 its 	 tempe rature 	 is 	 greater 	 than 	
4ºC. 	 In 	 the 	 range 	 0ºC 	 to 	 4ºC 	 water 	 contracts 	 on	 heatin g 	 and 	 expands 	 on	
cooling, 	i.e., 	negative.
(2)	 At 	 4ºC, 	 density 	 of 	 water 	 is 	 maximum	 while 	 its 	 specific 	 volume 	 is	
minimum.
8.6 Expansion of Gases
Gases 	 have 	 no	 definite 	 shape, 	 therefore 	 gases 	 have 	 only 	 volume 	 expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : 	 It 	 is 	 defined 	 as 	 the 	 amount 	 of 	 heat 	 required 	 to 	 raise 	
the 	temperature	of 	the 	whole 	body	(mass, 	m )	through 	1ºC 	or 	1	K.
Thermal 	c apacity 	= 	m c 	= 	µ C 	= 	
Dimension	: 	[ML
2
T
–2
?
–1
], 	Unit 	: 	call 	ºC 	(practical) 	Joule 	K 	(S.I.)
(2) Water Equivalent :	 W ater 	 equivalent 	 of	 a 	 body 	 is	 defined 	 as	 the 	 mass 	 of	
water 	 which 	 would	 absorb 	 or 	 evolve 	 the 	 same 	 amount 	 of 	 heat 	 as 	 is 	 done 	
by 	 the 	 body	 in 	 rising 	 or 	 falling 	 through 	 the 	 same 	 range 	 of 	 temperature. 	
It 	is 	represented 	by	 W .
If 	m 	= 	Mass 	of 	the 	body ,	c 	= 	Specific 	heat 	of 	 body
? 	 W ater 	equivalent	( W) 	= 	mc gm
8.8 Specific Heat
(1) Gram specific heat : 	 The	 heat 	 required 	 to 	 raise 	 the 	 temperature 	 of 	 one 	
gram 	 mass 	 of 	 a 	 body	 through 	 1ºC 	 (or 	 1	 K)	 is 	 called 	 gram 	 specific 	 heat 	
of 	the 	material 	of 	the 	body .
specific 	heat, 	 c	=	
Page 4


Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND 
CALORIEMETRY
8.1 Heat
The	 ener gy 	 associated 	 with 	 configuration 	 and 	 random 	 motion 	 of 	 the 	 atoms 	
and	 molecules 	with 	in 	a 	body	is 	called 	heat.
(1)	 Units 	: 	Joule 	(S.I.) 	and 	calorie 	(Practical 	unit)
(2)	 The 	ratio 	 of 	work	done 	(W) 	to 	heat 	produced 	(Q) 	 is 	constant.
J 	is 	called 	mechanical 	equivalent	of 	heat 	and 	has 	v alue 	4.2	J/cal. 	
1	calorie	 = 	4.186	Joule 	= 	4.12	Joule
(3)	 Heat 	 is 	 a 	 path 	 dependent 	 and 	 is 	 taken 	 to 	 be 	 positive 	 if 	 the 	 system 	 absorbs 	
it 	and 	negative 	if 	releases 	it.
8.2 Temperature
T emperature 	 is 	 defined 	 as 	 the 	 degree 	 of 	 hotness 	 or 	 coldness 	 of 	 a 	 body .	 Heat 	
flows 	from 	higher 	temperature 	to 	lower 	temperature.
T wo 	bodies 	are 	said 	to 	be 	in 	thermal 	equilibrium 	when 	both 	the 	bodies 	are 	
at	the 	same 	temperature. 	 T emperature 	a 	kinetic 	ener gy 	
8.3 Scales of Temperature
The 	 K elvin 	 temperature 	 s cale 	 is 	 als o 	 know n 	 as 	 thermodynamic 	 s cale. 	 The 	 S .I.	
unit 	 of 	 temper ature 	 is 	 kelvi n 	 and 	 is 	 defined 	 as 	 (1/273.16) 	 of 	 the 	 temperature	
of	 the 	 triple 	 point 	 of 	 water . 	 The	 triple	 point 	 of 	 water 	 is 	 that 	 point 	 on	 a 	 P–T 	
diagram 	 where 	 the 	 three 	 phases 	 of 	 water , 	 the 	 solid, 	 the 	 liquid 	 and 	 the 	 gas, 	
can	 coexist 	in 	thermal 	equilibrium.
T o 	 construct 	 a 	 scale 	 of 	 temperature, 	 two	 fixed	 points 	 are 	 taken. 	 First 	 is 	 the 	
freezing 	 point 	 of 	 water ,	 it 	 is 	 called 	 lower 	 fixed 	 point.	 The 	 second 	 is 	 the 	 boiling	
point 	of 	water ,	it 	is 	calle d 	upper 	fixed	point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius	 ºC	 0ºC	 100ºC	 100
Fahrenheit	 ºF	 32ºF	 212ºF	 180
Reaumer	 ºR	 0ºR	 80ºR	 80
Rankine	 ºRa	 460 	Ra	 672 	Ra	 212
Kelvin	 K	 273.15 	K	 373.15 	K	 100
T emperature 	 on	 one 	 scale 	 can 	 be 	 converted 	 into 	 other 	 scale 	 by	 using 	 the 	
following 	identity .
	=	Constant 	for 	all	scales
8.4 Thermal Expansion
When 	matter 	is 	heated, 	it 	expands.
(i)	 Coefficient 	of 	linear 	expansion 	a 	= 	
(ii)	 Coefficient 	of 	superficial 	expansion 	 ß 	= 	
(iii)	 Coefficient 	of 	volume 	expansion 	 ? 	= 	
(iv)	 The 	 value 	 of 	a, ß and ? 	 depends 	 upon	 the 	 nature 	 of 	 material. 	 All 	 have 	 
dimension 	[?
–1
] a nd 	unit 	per 	ºC.
(v)	 ? L 	= 	La?T,	?A 	=	Aß?T and ?V 	=	 V??T
(vi)	 Final 	length	 L ’ 	 =	 L 	+ 	? L 	= 	L 	(1 	+ 	a?T)
Final 	area 	 A ’ 	 =	 A 	+ 	? A 	= 	 A 	(1 	+ 	ß?T)
Final 	volu me	 V’ 	 =	 V 	+ 	? V 	= 	 V 	(1 	+ 	??T)
(vii) 	ß 	= 	2	a and ? = 	3	a
8.5 Anomalous Expansion of Water
(1)	 In 	case 	 of 	 water , 	 it 	 expands 	 on	 heating 	 if 	 its 	 tempe rature 	 is 	 greater 	 than 	
4ºC. 	 In 	 the 	 range 	 0ºC 	 to 	 4ºC 	 water 	 contracts 	 on	 heatin g 	 and 	 expands 	 on	
cooling, 	i.e., 	negative.
(2)	 At 	 4ºC, 	 density 	 of 	 water 	 is 	 maximum	 while 	 its 	 specific 	 volume 	 is	
minimum.
8.6 Expansion of Gases
Gases 	 have 	 no	 definite 	 shape, 	 therefore 	 gases 	 have 	 only 	 volume 	 expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : 	 It 	 is 	 defined 	 as 	 the 	 amount 	 of 	 heat 	 required 	 to 	 raise 	
the 	temperature	of 	the 	whole 	body	(mass, 	m )	through 	1ºC 	or 	1	K.
Thermal 	c apacity 	= 	m c 	= 	µ C 	= 	
Dimension	: 	[ML
2
T
–2
?
–1
], 	Unit 	: 	call 	ºC 	(practical) 	Joule 	K 	(S.I.)
(2) Water Equivalent :	 W ater 	 equivalent 	 of	 a 	 body 	 is	 defined 	 as	 the 	 mass 	 of	
water 	 which 	 would	 absorb 	 or 	 evolve 	 the 	 same 	 amount 	 of 	 heat 	 as 	 is 	 done 	
by 	 the 	 body	 in 	 rising 	 or 	 falling 	 through 	 the 	 same 	 range 	 of 	 temperature. 	
It 	is 	represented 	by	 W .
If 	m 	= 	Mass 	of 	the 	body ,	c 	= 	Specific 	heat 	of 	 body
? 	 W ater 	equivalent	( W) 	= 	mc gm
8.8 Specific Heat
(1) Gram specific heat : 	 The	 heat 	 required 	 to 	 raise 	 the 	 temperature 	 of 	 one 	
gram 	 mass 	 of 	 a 	 body	 through 	 1ºC 	 (or 	 1	 K)	 is 	 called 	 gram 	 specific 	 heat 	
of 	the 	material 	of 	the 	body .
specific 	heat, 	 c	=	
Units 	: 	Calorie/gm ºC	(Practical), 	J/kg 	K(S.I.)
Dimension 	: 	[L
2
T
–2
?
–1
]
(2) Molar specific heat : 	 Amount 	 of 	 heat 	 required 	 to 	 raise 	 the 	 temperature 	
of 	 one 	 gram 	 mole 	 of 	 the 	 substance 	 through 	 a 	 unit 	 degree 	 it 	 is 	 represented 	
by 	(capital) 	C.
? 	 C	 =	
Units 	: 	Cal 	mol
–1
	ºC
–1
	(Practical), 	J 	mol
–1
 K
–1
	(S.I.)
Dimension 	: 	[ML
2
T
–2
?
–1
µ
–1
]
8.9 Specific Heat of Solids
Specific 	heat 	of 	 a 	solid 	is 	specific 	heat 	at 	constant 	volume 	C
v
.
W ith 	rise 	in 	temperature,	C
v
	increases 	and 	becomes 	co nstant 	= 	3R
Dulong and Petit law : 	 A verage 	 molar 	 specific 	 heat 	 of 	 all 	 metals	 at 	 room 	
temperature 	 is 	 constant	 and 	 is 	 equal 	 to 	 3R. 	 This 	 statement 	 is 	 known 	 as 	 Dulong	
and	 Petit 	law .
8.10 Latent Heat
(1)	 When 	 a 	 substance 	 changes 	 from 	 one 	 state 	 to 	 another 	 state 	 then 	 ener gy 	
is 	either 	absorbed 	or 	liber ated. 	 This 	heat 	ener gy 	is 	called 	latent 	heat.
(2)	 No 	 change 	 in 	 tempera ture 	 is 	 involved 	 when 	 the 	 substance 	 changes 	 its 	
state.
(3) ? Q 	= 	m L, 	where 	L 	is 	the 	latent 	heat.
(4)	 Unit 	: 	 cal/gm 	or 	J 	kg	and 	Dimension 	: 	[L
2
T
–2
]
(5)	 Any 	 material 	has 	two	types 	of 	latent 	heats
(i) Latent heat of fusion : 	 The	 heat 	 required 	 to 	 change 	 1	 kg	 of 	 the 	
material 	 in 	 its 	 solid 	 state 	 to 	 its 	 liquid 	 state, 	 latent 	 heat 	 of 	 fusion 	 (or 	
latent 	heat 	of 	ice) 	is 	L
F
	= 	L
ice
 ˜ 	80	cal/g.
Page 5


Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND 
CALORIEMETRY
8.1 Heat
The	 ener gy 	 associated 	 with 	 configuration 	 and 	 random 	 motion 	 of 	 the 	 atoms 	
and	 molecules 	with 	in 	a 	body	is 	called 	heat.
(1)	 Units 	: 	Joule 	(S.I.) 	and 	calorie 	(Practical 	unit)
(2)	 The 	ratio 	 of 	work	done 	(W) 	to 	heat 	produced 	(Q) 	 is 	constant.
J 	is 	called 	mechanical 	equivalent	of 	heat 	and 	has 	v alue 	4.2	J/cal. 	
1	calorie	 = 	4.186	Joule 	= 	4.12	Joule
(3)	 Heat 	 is 	 a 	 path 	 dependent 	 and 	 is 	 taken 	 to 	 be 	 positive 	 if 	 the 	 system 	 absorbs 	
it 	and 	negative 	if 	releases 	it.
8.2 Temperature
T emperature 	 is 	 defined 	 as 	 the 	 degree 	 of 	 hotness 	 or 	 coldness 	 of 	 a 	 body .	 Heat 	
flows 	from 	higher 	temperature 	to 	lower 	temperature.
T wo 	bodies 	are 	said 	to 	be 	in 	thermal 	equilibrium 	when 	both 	the 	bodies 	are 	
at	the 	same 	temperature. 	 T emperature 	a 	kinetic 	ener gy 	
8.3 Scales of Temperature
The 	 K elvin 	 temperature 	 s cale 	 is 	 als o 	 know n 	 as 	 thermodynamic 	 s cale. 	 The 	 S .I.	
unit 	 of 	 temper ature 	 is 	 kelvi n 	 and 	 is 	 defined 	 as 	 (1/273.16) 	 of 	 the 	 temperature	
of	 the 	 triple 	 point 	 of 	 water . 	 The	 triple	 point 	 of 	 water 	 is 	 that 	 point 	 on	 a 	 P–T 	
diagram 	 where 	 the 	 three 	 phases 	 of 	 water , 	 the 	 solid, 	 the 	 liquid 	 and 	 the 	 gas, 	
can	 coexist 	in 	thermal 	equilibrium.
T o 	 construct 	 a 	 scale 	 of 	 temperature, 	 two	 fixed	 points 	 are 	 taken. 	 First 	 is 	 the 	
freezing 	 point 	 of 	 water ,	 it 	 is 	 called 	 lower 	 fixed 	 point.	 The 	 second 	 is 	 the 	 boiling	
point 	of 	water ,	it 	is 	calle d 	upper 	fixed	point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius	 ºC	 0ºC	 100ºC	 100
Fahrenheit	 ºF	 32ºF	 212ºF	 180
Reaumer	 ºR	 0ºR	 80ºR	 80
Rankine	 ºRa	 460 	Ra	 672 	Ra	 212
Kelvin	 K	 273.15 	K	 373.15 	K	 100
T emperature 	 on	 one 	 scale 	 can 	 be 	 converted 	 into 	 other 	 scale 	 by	 using 	 the 	
following 	identity .
	=	Constant 	for 	all	scales
8.4 Thermal Expansion
When 	matter 	is 	heated, 	it 	expands.
(i)	 Coefficient 	of 	linear 	expansion 	a 	= 	
(ii)	 Coefficient 	of 	superficial 	expansion 	 ß 	= 	
(iii)	 Coefficient 	of 	volume 	expansion 	 ? 	= 	
(iv)	 The 	 value 	 of 	a, ß and ? 	 depends 	 upon	 the 	 nature 	 of 	 material. 	 All 	 have 	 
dimension 	[?
–1
] a nd 	unit 	per 	ºC.
(v)	 ? L 	= 	La?T,	?A 	=	Aß?T and ?V 	=	 V??T
(vi)	 Final 	length	 L ’ 	 =	 L 	+ 	? L 	= 	L 	(1 	+ 	a?T)
Final 	area 	 A ’ 	 =	 A 	+ 	? A 	= 	 A 	(1 	+ 	ß?T)
Final 	volu me	 V’ 	 =	 V 	+ 	? V 	= 	 V 	(1 	+ 	??T)
(vii) 	ß 	= 	2	a and ? = 	3	a
8.5 Anomalous Expansion of Water
(1)	 In 	case 	 of 	 water , 	 it 	 expands 	 on	 heating 	 if 	 its 	 tempe rature 	 is 	 greater 	 than 	
4ºC. 	 In 	 the 	 range 	 0ºC 	 to 	 4ºC 	 water 	 contracts 	 on	 heatin g 	 and 	 expands 	 on	
cooling, 	i.e., 	negative.
(2)	 At 	 4ºC, 	 density 	 of 	 water 	 is 	 maximum	 while 	 its 	 specific 	 volume 	 is	
minimum.
8.6 Expansion of Gases
Gases 	 have 	 no	 definite 	 shape, 	 therefore 	 gases 	 have 	 only 	 volume 	 expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : 	 It 	 is 	 defined 	 as 	 the 	 amount 	 of 	 heat 	 required 	 to 	 raise 	
the 	temperature	of 	the 	whole 	body	(mass, 	m )	through 	1ºC 	or 	1	K.
Thermal 	c apacity 	= 	m c 	= 	µ C 	= 	
Dimension	: 	[ML
2
T
–2
?
–1
], 	Unit 	: 	call 	ºC 	(practical) 	Joule 	K 	(S.I.)
(2) Water Equivalent :	 W ater 	 equivalent 	 of	 a 	 body 	 is	 defined 	 as	 the 	 mass 	 of	
water 	 which 	 would	 absorb 	 or 	 evolve 	 the 	 same 	 amount 	 of 	 heat 	 as 	 is 	 done 	
by 	 the 	 body	 in 	 rising 	 or 	 falling 	 through 	 the 	 same 	 range 	 of 	 temperature. 	
It 	is 	represented 	by	 W .
If 	m 	= 	Mass 	of 	the 	body ,	c 	= 	Specific 	heat 	of 	 body
? 	 W ater 	equivalent	( W) 	= 	mc gm
8.8 Specific Heat
(1) Gram specific heat : 	 The	 heat 	 required 	 to 	 raise 	 the 	 temperature 	 of 	 one 	
gram 	 mass 	 of 	 a 	 body	 through 	 1ºC 	 (or 	 1	 K)	 is 	 called 	 gram 	 specific 	 heat 	
of 	the 	material 	of 	the 	body .
specific 	heat, 	 c	=	
Units 	: 	Calorie/gm ºC	(Practical), 	J/kg 	K(S.I.)
Dimension 	: 	[L
2
T
–2
?
–1
]
(2) Molar specific heat : 	 Amount 	 of 	 heat 	 required 	 to 	 raise 	 the 	 temperature 	
of 	 one 	 gram 	 mole 	 of 	 the 	 substance 	 through 	 a 	 unit 	 degree 	 it 	 is 	 represented 	
by 	(capital) 	C.
? 	 C	 =	
Units 	: 	Cal 	mol
–1
	ºC
–1
	(Practical), 	J 	mol
–1
 K
–1
	(S.I.)
Dimension 	: 	[ML
2
T
–2
?
–1
µ
–1
]
8.9 Specific Heat of Solids
Specific 	heat 	of 	 a 	solid 	is 	specific 	heat 	at 	constant 	volume 	C
v
.
W ith 	rise 	in 	temperature,	C
v
	increases 	and 	becomes 	co nstant 	= 	3R
Dulong and Petit law : 	 A verage 	 molar 	 specific 	 heat 	 of 	 all 	 metals	 at 	 room 	
temperature 	 is 	 constant	 and 	 is 	 equal 	 to 	 3R. 	 This 	 statement 	 is 	 known 	 as 	 Dulong	
and	 Petit 	law .
8.10 Latent Heat
(1)	 When 	 a 	 substance 	 changes 	 from 	 one 	 state 	 to 	 another 	 state 	 then 	 ener gy 	
is 	either 	absorbed 	or 	liber ated. 	 This 	heat 	ener gy 	is 	called 	latent 	heat.
(2)	 No 	 change 	 in 	 tempera ture 	 is 	 involved 	 when 	 the 	 substance 	 changes 	 its 	
state.
(3) ? Q 	= 	m L, 	where 	L 	is 	the 	latent 	heat.
(4)	 Unit 	: 	 cal/gm 	or 	J 	kg	and 	Dimension 	: 	[L
2
T
–2
]
(5)	 Any 	 material 	has 	two	types 	of 	latent 	heats
(i) Latent heat of fusion : 	 The	 heat 	 required 	 to 	 change 	 1	 kg	 of 	 the 	
material 	 in 	 its 	 solid 	 state 	 to 	 its 	 liquid 	 state, 	 latent 	 heat 	 of 	 fusion 	 (or 	
latent 	heat 	of 	ice) 	is 	L
F
	= 	L
ice
 ˜ 	80	cal/g.
208
(ii) Latent heat of vaporisation : 	 The	 heat 	 ener gy 	 required 	 to	 change 	 1	
kg	 of 	 the 	 material 	 in 	 its 	 liquid 	 to 	 1	 kg	 of 	 the 	 material 	 in 	 its 	 gaseous 	
state. 	 Latent 	 heat 	 of 	 vaporisation 	 (latent 	 heat 	 of 	 steam) 	 is 	 L
v
	 =	 L
steam
 
˜ 	540	cal/gm.
8.11 Principle of Caloriemetry
Heat 	lost 	= 	Heat 	gained
i.e., 	 principle	 of	 caloriemetry 	 represents 	 the	 law 	 of	 conservation 	 of	 heat
ener gy .
8.12 Heating Curve
Thermodynamic Processes
(1) Thermodynamics : It 	 is 	 a 	 branch 	 of 	 science 	 which 	 deals 	 with 	 exchange 	
of 	 heat 	 ener gy 	 between 	 bodies 	 and 	 conversion 	 of 	 the 	 heat 	 ener gy 	 into 	
mechanical 	ener gy 	and 	vice 	versa.
(2) Thermodynamic system : 	 A 	 collection 	 of 	 an 	 extremely 	 lar ge 	 number 	
of 	 atoms 	 or 	 molecules 	 confi ned	 w ith 	 in 	 certain 	 boundaries 	 s uch 	 that 	
it 	 has 	 a 	 certai n 	 value 	 of 	 pressure, 	 volume 	 and 	 temperature 	 is 	 called 	 a 	
thermodynamic 	 system. 	 Anything 	 outside 	 the 	 thermodynamic 	 system 	 to 	
which	ener gy 	or 	matter 	is 	exchanged 	is 	called 	its 	surroundings.
Thermodynamic 	system 	may 	be 	of 	three 	types 	:
(i) Open system : 	 It 	 exchange 	 both 	 energy 	 and 	 matter 	 with 	 the	
surrounding.
(ii) Closed system : 	 It 	 e xc ha ng e 	 onl y 	 e ne r gy 	 (not	 m a t t e r ) 	 wi t h	 t he	
surroundings.
(iii) Isolated system : It 	 exchange 	 neither 	 ener gy 	 nor 	 matter 	 with 	 the 	
surrounding.
Heat 	(Q)