Thermodynamics (PHYS2140)
BSc, Physics - PHYS
Semester: First Semester
Level: 200
Year: 2018
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE DEPARTMENT OF PHYSICS
Thermodynamics: PHYS2I4O Tutorial Sheet 2
Exercise 1
The equilibrium state of a pure substance is characterized by a state equation of the form
f (p, V ,T)= 0. The
heat received by this system in the reversible elementary process, is a differential
form of independent
variables. Then for a
mole
of the substance, Q =C
v
dT +ldV = C
p
dT + hdp = + dV ,
where C
v
, C
p
, l, h, are called calorimetric coefficients of the system.
1. Express the coefficients 1, h, and in terms of C
v
, C
p
and of the material properties
a and
2. Assuming =
find the relation between the isothermal compression coefficient
r
and the adiabatic compression coefficient
s
.
Considering that the substance receives only work from the pressure forces, express the
following relations starting by the fact that dU and dS are total differentials:
l = T
and h = -T
then
= T
and
= -T
Exercise 2
The state equation of a real gas is written
+
(V —b) = RT, where R = 8.3J/mol.
o
K
a= 41.4Pa.c K.m
6
/mol SI and b= 3.3x 1 0
-5
m
3
/mol. The molar specific heat at constant
volume is equal to C
v
=
R whatever the temperature when its pressure tends to zero,
1) Calculate the value of C
v
at temperature T, when the molar volume of gas is held to
be V.
2) Calculate the variation ∆C
v
when the molar volume passes from V
o
to 2V
o
at constant
temperature. V
o
= 20 liters, T= 300°K.
Exercise 3
1) One compresses isothermally a diatomic ideal gas (y =1.41) from pressure
p
o
=
1atm
to p
i
=20atm at the temperature T
o
= 273°K . The gas is then released adiabatically in
the reversible process until pressure p
0
= 1atm . Find the final temperature T
1
after this
double operation.
2)One restarts the previous operation at constant temperature T1. Find the new
temperature T
2
of gas.
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3) Find the general term of temperature T
n
of gas reached at the end of n successive
double operations described previously.
4) Find the change in internal energy after operations.
Exercise 4
One has one source of temperature T
A
. In relation with this source of heat, a
monoatomic perfect gas performs a cyclic process represented in the Clapeyron diagram.
The cycle is composed of an adiabatic process (A→B), an isochore process (B→C)
a
nd
an isothermal process (C→A). All these transformations are considered as
reversible. The initial state variable are p
A
, V
A
and T
A
. After the adiabatic process, V
B
=
2V
A
.
1. Determine the conditions (p, V, T) in B and C in terms of p
A
, V
A
and T
A
2. Find the expressions of heat Q, work W and the change in internal energy∆U of each
process in the cycle in terms of p
A
, V
A
and T
A
. Find the efficiency of the cycle =
|"|
#
Exercise 5
I. Express the elementary change in entropy of an ideal gas in terms of independent
variables T and V.
2. Deduce the change in entropy of one mole when the initial temperature and initial volume
are tripled simultaneously $=
%
and R= 8.32 SI.
Exercise 6
A metal of mass m= I kg, of specific heat capacity c
p
=880J/f kg °K at constant pressure and of
temperature T
o
= 27°C is set in contact with a source of heat of temperature T,=100°C .
After a certain time, the metal is in thermal equilibrium with the source.
1. Determine the change in entropy of metal.
2. Determine the change in entropy of univers.
Exercise 7
Air of mass 1 kg is considered as a perfect gas, is undergoing a Carnot cycle ABCDA. Two
isotherms AB and CD and two adiabats BC and DA in the reversible process. The
temperature at point A is Ti = 300 oK the pressures at points A, B and C are respectively p1
=1atm, P2 =3atm and p3 = 9atm. Take
c
p
= 10-3 J/kg.k, $=
%
and
&
'
/%
I. Calculate the thermodynamic efficiency of the cycle
2. Calculate the change in entropy of air of each process in the cycle
.
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Exercise 8
1) One mixes at constant pressure a mass m
1
= 0.5 kg of oil at temperature T
1
= 77 °C, with a
mass m
2
= 2kg 0f oil at T2 = 17 °C. Determine the change in entropy of the system. The
specific heat of oil is c
p
= 2.1J/g.
o
C.
2) One mixes at the atmospheric pressure a mass M
1
= 10 kg of water at temperature T
1
=
21
o
C, with a mass M
2
= 1 kg of ice at T
2
= -10
o
C. Determine the equilibrium temperature T
and the change in entropy of the system.,
1
1'he specific heat of water is c
1
=4.2J / g.
o
C, the
specific heat of ice G
2
= 2.15J I g.°C and the latent heat of fusion of ice at T
o
= 273
0
K is L =
336J/ g
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