Page 19 - Hsslive-Plus-One-Physics-Class-Notes-Part-III (1)

Heat, Thermodynamics & Kinetic Theory {18} Vinodkumar M, St. Aloysius H.S.S, Elthuruth, Thrissur.

 U 3 3 5
C   R But C - C = R So C = C + R. C  R R  R
V
P
 T 2 P V P V 2 2
5
C 2 R 5
  P  
C 3 3
V R
2
2. Diatomic gas.
They have three translational and two rotational degrees of freedom. So the internal energy of a mole of such
5 5  U 5
a gas is U  R T Therefore, U  R T But C   R
V
2 2  T 2
7 R
5 7 C P 2 7
C  C  R  R R  R Therefore,    5 
P
V
2 2 C V 2 R 5
7
If a diatomic molecule has in addition a vibrational mode also, then total internal energy U  RT ;
2

7  U 7 7 9
U  R T C   R But C  C  R  R  R  R
P
V
P
2  T 2 2 2
9
C R 9
  P  2 
Therefore,
C 7 R 7
V 2
Specific heat capacity of solids
Solid atoms are vibration about its mean position. An oscillator in one dimension has an average energy of
1
2
K T  K T . In three dimension, average energy = 3 K T. So the total energy/mole of a solid is ,
B
B
2 B
U
U = 3 K T x N A = 3 R T. So  C  3 R
V
B T
Specific heat capacity of water.
We treat water like a solid. For each atom, the average energy is 3 K T. Water molecule has three atoms.
B
So total internal energy for one mole of water = 3 x 3 K T x N A = 3 x 3 R T = 9 R T.
B
U
Therefore,  C  9 R .
V
T
Newtons laws of cooling
According to Newton’s law of cooling the rate of loss of heat is directly proportional to difference of
temperature between the body and its surroundings.

dQ
 K(T  T ) . TT is temperature of surrounding medium and T is temperature of body. K is constant that
2
1
dT 1 2
depends on nature of surface and area of exposed surface.
Note: (1) The law is applicable for small temperature difference.
(2) For small temperature difference, cooling occurs
due to a combination of
conduction, convection and radiation.
(3) The graph between difference in temperature and time is as shown in figure.
Poission’s Ratio
When a wire is stretched, there will be a decrease in diameter of the wire. The strain perpendicular to the
applied force is called lateral strain. According to Simon Poisson, within elastic limit, lateral strain is propor-