The document discusses key concepts in thermodynamics including: 1. Thermal equilibrium and the zeroth law of thermodynamics which states that two bodies in contact will reach the same temperature. 2. Degrees of freedom for different types of gases and the law of equipartition of energy. 3. Specific heat capacities including molar heat capacities Cv and Cp. 4. Different types of thermodynamic processes including isobaric, isochoric, isothermal, and adiabatic processes. 5. The first law of thermodynamics which is a statement of conservation of energy. 6. Heat engines and the second law of thermodynamics as expressed by both the Kelvin

1. BATCH
BASIC MATHS
THERMODYNAMICS

2. Thermal Equilibrium
&
Zeroth Law of ThermoDynamics

3. Thermal Equilibrium
When all macroscopic properties like
Pressure(P),Volume(V),Temperature(T),mass(m),number
of moles(n) are constant and do not change with time
A body is said to be in
thermal equilibrium
with its surrounding if
it is insulated
completely

4. Two bodies in contact in Thermal
Equilibrium

5. ZEROTH LAW OF THERMODYNAMICS
1. A & C kept in contact ⇒ after
some time A & C will be in a
thermal equilibrium TA=TC
2. B & C are kept in contact ⇒ after
some time , thermal equilibrium
TB=TC

6. Initial Energy(U) , DOF
&
Molar Specific Heat Capacities

7. Initial Energy(U)

8. For an ideal gas at Rest,

9. Degree of freedom (𝒇)
Degree of freedom (DOF or 𝒇) is the number of
independent ways in which a molecule possesses
translational, rotational and vibratory motion.
OR
The number of independent terms in the expression for
kinetic Energy (not dependent on each other)

10. Monoatomic gas: (ex: He,Ne,Ar,…..)
Diatomic gas: (ex: O2,N2,H2,…..)

11. Polyatomic gas: (ex: SO2,CO2,CH4,NH3…..)
i) Linear
ii) Non-Linear

12. Q1)

13. Q2)

14. Law of Equipartition of Energy
The average Kinetic Energy associated with each degree of
freedom of a molecule is
𝟏
𝟐
KT , where K is R/N and T is
measured in Kelvin

16. Internal Energy and change in Internal
Energy

17. Q3)

18. a) 1000 R
b) 2000 R
c) 2500 R
d) 3000 R
Q4) Find the K.E. of 4 moles N2 at 27 oC

19. a)
𝟑
𝟐
RT
b)
𝟏
𝟒
RT
c) 𝟒 RT
d) 𝟐 RT
Q5) Find the K.E. of 3.2 g O2 at temperature T kelvin.

20. Q6)

21. Q7)

22. Specific Heat & Molar Specific Heat

23. Cv & Cp
CV – Molar S.H.C at Constant Volume
CP – Molar S.H.C at Constant Pressure

24. Cv & Cp in terms of f

25. Q8) Find Molar Cv, Cp, Cp-Cv for O2. Also calculate Cp-Cv (S.H.C
per unit Mass) for O2.

26. Q9)

27. Q10)

28. Cp / Cv

29. i. Monoatomic
ii. Diatomic
iii. Polyatomic

30. Cp & Cv in terms of R & Y

32. Q11)

33. Q12)

34. Q13)

35. Q14)

36. Q15)

37. Q16)

38. Work , Internal Energy and Heat
in Thermodynamics

39. Work in Thermodynamics

40. Sign of Work

41. Units of P,V and Work

42. a) 2.5 ergs
b) 250 J
c) 25 J
d) 250 N
Q17) A gas expands 0.25m3 at constant pressure 103 N/m2,
the work done is-

43. Work done by P-V curve

44. Q18)

45. Work is path dependent : Not a state Function

46. Work done in cyclic Process

47. Q19)

48. a) 4PoVo
b) -4PoVo
c) -22/7 PoVo
d) -13PoVo
Q20)

49. Q21)

52. Internal Energy (U)
1) U= P.E of molecules + KE of molecules
2) For ideal gas
𝑼 =
∆𝑼

53. For gases
1) U is a state function
2) U depends only on Temperature
3) ∆U depends only on ∆ T
4) ∆U is path independent
5) ∆U in closed cycle is Zero.

54. ∆𝑼 from P-V Curve

55. ∆𝑼 𝒊𝒏 𝒕𝒆𝒓𝒎𝒔 𝒐𝒇 𝑷𝑽

56. Q22)

58. Heat (∆Q) : Not a state Function
1) In terms of specific heat
2) In terms of Molar Specific Heat
3) At Constant Volume
4) At Constant Pressure

59. Sign of Heat (∆Q)

60. First Law of Thermodynamics

61. First Law of Thermodynamics
➢ It is a statement of Conservation of Energy

62. Q23)

63. Q24)

64. Q25)

65. Q26)

66. Q27)

69. Q28)

70. Q29)

72. Q30)

74. Types of Processes in Thermodynamics
1. Isobaric
2. Isochoric
3. Isothermal
4. Adiabatic

75. Isobaric Process
1. P= Constant
2. Charle’s Law:

76. 3. Graphs for Isobaric Process

77. 4. Molar S.H.C
5. ∆Q=
6. ∆U=
7. W=

78. 8. W: ∆Q: ∆U

79. a) 5:3:2
b) 5:2:3
c) 7:5:2
d) 7:2:5
Q31) Heat is supplied to a diatomic gas at constant pressure.
The ratio of ∆𝑸: ∆𝑼: ∆𝑾 is [AIIMS 1996]

80. a) 2/5
b) 3/5
c) 3/7
d) 5/7
Q32) When an ideal diatomic gas is heated at constant
pressure,the fraction of the heat energy supplied which
increases the internal energy of the gas is
[IIT 1990;UPSEAT 1998;RPET 2000]

81. a) 2/5
b) 2/3
c) 1/3
d) 2/7
Q33) The volume (V) of a monoatomic gas varies with its
temperature(T),as shown in the graph. The ratio of work done
by the gas,to the heat absorbed by it, when it undergoes a
change from state A to state B,is [NEET 2018]

82. Q34)

83. Isochoric Process
1. V=Constant
2. P ∝ T

84. 3. Graphs for Isochoric Process

85. 4. Molar S.H.C
5. ∆Q=
6. ∆U=
7. W=

86. Isothermal Process
i. very very slowly
ii. Perfectly conducting boundary
1. T=constant
2. Boyle’s Law

87. Graphs for Isothermal Process
1.

88. 2. 3.

89. 4. Molar S.H.C
5. ∆U=
6. W=

91. Q35)

92. a) 5RT loge 2
b) -5RT loge 2
c) RT loge 10
d) -RT loge 10
Q36) Five moles of an ideal gas is compressed from 2V to V
isothermally at ‘T’ kelvin. Find the work done in the process.

93. Adiabatic Process
i. very rapidly
ii. Perfectly insulating boundary
1. ∆Q= 0
2. PV𝜸= Constant

95. 3. Graph for Adiabatic Process

96. Slope of PV for Isothermal v/s Adoabtic

97. 4. Molar S.H.C
5. ∆Q=
6. ∆U=

98. Q37)

99. Q38)

100. Q39)

102. Q40)

104. Q41)

106. Q42)

108. Comparison of different Processes
EXPANSION

109. COMPRESSION

110. Q43)

111. Q44)

112. Q45)

113. Q46)

114. 2nd Law of Thermodynamics

115. Heat Engine

116. 2nd Law of Thermodynamics
Kelvin-Planck Statement:
No process is possible whose sole result is the
absorption of heat from a reservoir and the complete
conversion of heat into work.

117. Carnot’s Heat Engine
No Heat Engine operating between
same Temperatures (T1 & T2) can
have efficiency more than Carnot’s
Heat Engine
Ideal Heat Engine 𝜼 →Max for Carnot’s
Heat Engine

118. Four Process in Carnot’s Heat Engine

119. Carnot’s Heat Engine : P-V Curve

121. Q47)

122. Q48)

123. Q49)

124. Q50)

126. Q51)

128. Q52)

130. Refrigerator

131. Coeffecient of Performance

132. Clausius Statement
No process is possible whose sole result is the transfer of
heat from a colder object to a hotter object.
2nd Law of Thermodynamics

133. Q53)

134. Q54)

136. Q55)

138. Q56)