1. Xtra Edge February 2012 - Career Point

PHYSICS FUNDAMENTAL FOR IIT-JEE
Thermal Expansion, Thermodynamics
Thermal Expansion :
.(a) When the temperature of a substance is increased,
it expands. The heat energy which is supplied to
the substance is gained by the constituent
particles of the substance as its kinetic energy.
Because of this the collisions between the
constituents particles are accompanied with
greater force which increase the distance between
the constituent particles.
∆l = lα∆T ; ∆A = Aβ∆T ; ∆V = Vγ∆T
or l' = l (1 + α∆T) ; A' = A(1 + β∆T) ;
V' = V(1 + γ∆T)
(b) Also ρ = ρ'(1 + γ∆T) where ρ' is the density at
higher temperature clearly ρ' < ρ for substances
which have positive value of γ
* β = 2α and γ = 3α
Water has negative value of γ for certain temperature
range (0º to 4ºC). This means that for that
temperature range the volume decreases with
increase in temperature. In other words the density
increases with increase in temperature.
30 ml
25 ml
20 ml
15 ml
10 ml
5 ml
0 ml
If a liquid is kept in a container and the temperature
of the system is increased then the volume of the
liquid as well as the container increases. The
apparent change in volume of the liquid as shown by
the scale is
∆Vapp = V(γ – 3α) ∆T
Where V is the volume of liquid at lower temperature
∆Vapp is the apparent change in volume
γ is the coefficient of cubical expansion of liquid
α is the coefficients of linear expansion of the
container.
Loss or gain in time by a pendulum clock with
1
change in temperature is ∆t = α(∆T) × t
2
KEY CONCEPTS & PROBLEM SOLVING STRATEGY
Where ∆t is the loss or gain in time in a time interval t
∆T is change in temperature and d is coefficient of
linear expansion.
If a rod is heated or cooled but not allowed to expand
or contract then the thermal stresses developed
F
= γα∆T.
A
If a scale is calibrated at a temperature T1 but used at
a temperature T2, then the observed reading will be
wrong. In this case the actual reading is given by
R = R0(1 + α∆T)
Where R0 is the observed reading, R is the actual
reading.
For difference between two rods to the same at all
temperatures l 1α1 = l2α2.
Thermodynamics
According to first law of thermodynamics
q = ∆U + W
For an isothermal process (for a gaseous system)
(a) The pressure volume relationship is ρV = constt.
(b) ∆U = 0
(c) q = W
(d) W = 2.303 nRT log10
V f
p
= 2.303 nRT i log10
Vi
pf
(e) Graphs T2 > T1
XtraEdge for IIT-JEE 25 FEBRUARY 2012
P
T2
T1
P
V
T
T
These lines are called isotherms (parameters at
constant temperature)
For an adiabatic process (for a gaseous system)
(a) The pressure-volume relationship is PV γ = constt.
(b) The pressure-volume-temperature relationship is
PV
= constt.
T
(c) From (a) and (b) TV γ–I = constt.
(d) q = 0
(e) W = –∆U
V