March 2011 - Career Point

PHYSICS FUNDAMENTAL FOR IIT-JEE
Calorimetry, K.T.G., Heat transfer
KEY CONCEPTS & PROBLEM SOLVING STRATEGY
Calorimetry :
The specific heat capacity of a material is the amount
of heat required to raise the temperature of 1 kg of it
by 1 K. This leads to the relation
Q = ms θ
where Q = heat supplied, m = mass, θ = rise in
temperature.
The relative specific heat capacity of a material is the
ratio of its specific heat capacity to the specific heat
capacity of water (4200 J kg –1 K –1 ).
Heat capacity or thermal capacity of a body is the
amount of heat required to raise its temperature by 1
K. [Unit : J K –1 ]
Thus heat capacity = Q/θ = ms
dθ 1 dQ
Also = ×
dt ms dt
i.e., the rate of heating (or cooling) of a body depends
inversely on its heat capacity.
The water equivalent of a body is that mass of water
which has the same heat capacity as the body itself.
[Unit : g or kg] This is given by
m×s
W =
s w
where m = mass of body, s = specific heat capacity of
the body, s w = specific heat capacity of water.
Principle of Calorimetry : The heat lost by one
system = the heat gained by another system. Or, the
net heat lost or gainsed by an isolated system is zero.
It system with masses m 1 , m 2 , ...., specific heat
capacities s 1 , s 2 , ...., and initial temperatures θ 1 , θ 2 , ....
are mixed and attain an equilibrium temperature θ
then
θ =
Σmsθ
, for equal masses θ =
Σms´
Σsθ
Σs
Newton's law of cooling :
The rate of loss of heat from a body in an
environment of constant temperature is proportional
to the difference between its temperature and that of
the surroundings.
If θ = temperature of the surroundings then
dθ
– ms = C´(θ – θ0 )
dt
where C´ is a constant that depends on the nature and
extent of the surface exposed. Simplifying
dθ C
= –C(θ – θ0 ) where C = = constant
dt
mś
Kinetic theory of gases :
The pressure of an ideal gas is given by p = 3
1 µnC
2
where µ = mass of each molecule, n = number of
molecules per unit volume and C is the root square
speed of molecules.
p = 3
1 ρC
2
or pV = 3
1 mC
2
where ρ is the density of the gas and m = mass of the
gas.
Root Mean Square Speed of Molecules :
This is defined as
2
2
2
C1 + C2
+ C3
+ ... + CN
C =
N
where N = total number of molecules. It can be
obtained through these relations
C =
3p
ρ
=
3RT
M
Total Energy of an ideal gas (E) :
This is equal to the sum of the kinetic energies of all
the molecules. It is assumed that the molecules do not
have any potential energy. This follows from the
assumption that these molecules do not exert any
force on each other.
1
E = mC 2 3 m 3
= RT = pV
2 2 M 2
Thus, the energy per unit mass of gas = 2
1 C
2
The energy per unit volume = 2
3 p
The energy per mole = 2
3 pV = 2
3 RT
2
XtraEdge for IIT-JEE 24 MARCH 2011