Page 1
Important Formulae
1. Thermodynamics
(i) Molar heat capacity C = heat required to raise the temperature of 1 mole of any substance by
1 °C or 1 K.
Q
nT
?
?
Q = nC ?T
Molar heat capacity of solids and liquids is almost constant. In case of gases C is process
dependent. It varies from 0 to ?. In isothermal process,
C = ? as ?T = 0
In adiabatic process,
C = 0 as Q = 0
C
p
(molar heat capacity of isobaric process) and C
v
(molar heat capacity of isochoric process) are
commonly used. In a general process pV
x
= constant, molar heat capacity is given by,
RR
C
1 1 x
??
? ? ?
(ii) First law of thermodynamics It is a law of conservation of energy given by,
Q = ?U + W
(iii) Detailed discussion of three terms of first law of thermodynamics
(a) Work done Following methods are generally used to find the work done,
Method 1
i
i
V
V
W pdV ?
?
(because dW = pdV)
Here, p should be either constant or function of V. If p is constant. It means process is isobaric,
W = p(V
f
– V
i
) = p ?V
Method 2 Work done can also be obtained by area under p-V diagram with projection on V-axis.
W = + ve as volume is increasing
W =
- ve as volume is decreasing
Page 2
Important Formulae
1. Thermodynamics
(i) Molar heat capacity C = heat required to raise the temperature of 1 mole of any substance by
1 °C or 1 K.
Q
nT
?
?
Q = nC ?T
Molar heat capacity of solids and liquids is almost constant. In case of gases C is process
dependent. It varies from 0 to ?. In isothermal process,
C = ? as ?T = 0
In adiabatic process,
C = 0 as Q = 0
C
p
(molar heat capacity of isobaric process) and C
v
(molar heat capacity of isochoric process) are
commonly used. In a general process pV
x
= constant, molar heat capacity is given by,
RR
C
1 1 x
??
? ? ?
(ii) First law of thermodynamics It is a law of conservation of energy given by,
Q = ?U + W
(iii) Detailed discussion of three terms of first law of thermodynamics
(a) Work done Following methods are generally used to find the work done,
Method 1
i
i
V
V
W pdV ?
?
(because dW = pdV)
Here, p should be either constant or function of V. If p is constant. It means process is isobaric,
W = p(V
f
– V
i
) = p ?V
Method 2 Work done can also be obtained by area under p-V diagram with projection on V-axis.
W = + ve as volume is increasing
W =
- ve as volume is decreasing
W = 0 as volume is constant
W = +ve as cyclic process is clockwise with p on y-axis.
(b) Change in internal energy ?U
?U = nC
V
?T
for all processes.
For this C
V
(or nature of gas), n and ?T should be known.
If either of the three terms is not known, we can calculate ?U by,
?U = Q - W
(c) Heat exchange Q
Q = nC ?T.
For this n, ?T and molar heat capacity C should be known. C is a process dependent. So,
if either of the three terms (n, ?T or C) is not known, we can calculate Q by,
0 = ?U + W
(iv)
dp p
x
dV V
?? in process pV
x
= constant
or slope of p-V graph =
p
x
V
?
In isobaric process x = 0, therefore slope = 0 In isothermal process x = 1, therefore slope =
p
V
?
In adiabatic process x = ?, therefore slope =
p
V
??
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