Thermodynamics (PHYS2140)
BSc, Physics - PHYS
Semester: First Semester
Level: 200
Year: 2018
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE DEPARTMENT OF PHYSICS
Fluid Mechanics: PHYS2140 Tutorial Sheet I
1
Thermodynamic
Exercise 1
The fluid equation of state of a given mass link pressure p, temperature T and volume V through is
p,V,T)=0
1. Demonstrate the following general relations between the partial derivations
= -1 and
2. Calculate the thermodynamic property of materials a, and x for an ideal gas
3. One mole of CO
2
gas obeys to the van der Waals' equation
.
(V -b)= RT , a and b are
constants and R the ideal gas constant. Express the coefficients and
y
in term of independent
variables V and T.
Exercise 2
Show that for any fluid, the coefficient and are linked by the relationship
= -
Exercise 3
One carbon dioxide CO2 obeying the van der Waals equation
.
(V - b)= RT is used in the gas
thermometer at constant pressure P
o
=10
5
N/M
2
Express the temperature θ pointed out by the thermometer in the form θ = t(1 + ɛ), where t is the Celsius
temperature.
Exercise 4
From the liquid benzene, a compression at a constant temperature T=1 0°C under the atmospheric
pressure What pressure p
1
is required to reduce the volume of benzene of 2% of its initial value v
o
? The
isothermal
repression coefficient at 10°C is = 9.3 x 10
-10
S.I.
Exercise 5
The differential of the pressure of a gas (nitrogen, between 0 and 40 atm) is given by the equation relative
to
a
mole
dp = -
!
"#
!
dT
Deduce the equation of state of gas in the interval of pressure above
Exercise 6
The experiments have shown that, the isobaric thermal expansion coefficient a and the isothermal
compression coefficient of one mole of a gas, is expressed in term of independent variables p and T.
it is written by the equations: a =
$%
and =
&$%'
www.schoolfaqs.net
where R and b are constants. Find the equation of state of this gas, relative to one mole.
Exercise 7
The mass unit of a real gas (CO
2
) obeys to the Berthelot equation
(
.
(V - b)= rT with
A = 5.75 x 10
4
, b = 9.73 x 10
-4
and r =189. For a certain critical temperature T
c
, the
corresponding
isotherm in the Clapeyron diagram (p, v) allows in a point C a horizontal tangent with a point of inflexion.
1. Deduce the critical temperature T
c
, the pressure pc and the volume vc of gas in C, in term of a, b and
r.
2. Write the state equation by introducing the reduced coordinates P
r
=
)
, v
r
=
*
and T
r
=
*
; then
conclude
Exercise 8
Determine the phase or phases in a system consisting of H
2
O at the following conditions and sketch p-v
and T-v diagrams showing the location of each state. Use a table of data.
a) p = 80 lbf/in.
2
, T = 3121.07
o
F e) p = 5 bar, T = 200
o
C
b) p = 80 lbf/in.
2
, T = 400
o
F f) T = 200
o
F p = 2.5 MPa
c) T = 400
o
F , p=80 lbf/in.
2
, g) T= 160
o
C, p = 4.8 bar
d) p = 5 bar, T = 151.9
o
F h) T = -12, p = 1 bar
e) Exercise 9
A two-phase liquid–vapor mixture of H
2
O has a temperature of 200°C and occupies a volume
of 0.05 m
3
. The masses
The masses of saturated liquid and vapor present are 0.75 kg and 2.26 kg respectively.
Determine the specific volume of the mixture, in m
3
/kg.
Exercise 10
Determine the volume, in ft
3
, occupied by 2/b of H
2
O at a pressure of 1000 lbf/in.
2
and
(a) A temperature of 600°F.
(b) A quality of 80%.
(c) A temperature of 200°F.
www.schoolfaqs.net
Exercise 11
A two-phase liquid–vapor mixture of H
2
O has a temperature of 300°C and occupies a volume
of 0.05 m
3
. The masses
The mas
s
es of saturated liquid and vapor present are 0.75 kg and 2.26 kg respectively.
Determine the specific volume of the mixture, in m
3
/kg.
Exercise 12
Two thousand kg of water initially a saturated liquid at 150
o
C, is heated in a closed, rigid tank to a final
state where the pressure, is 2,5 MPa, Determine the final temperature, in °C, the volume of the tank, in
m
3
, and ketch the process on T-v and p-v diagrams.
Exercise 13
Water vapor is heated in a closed, rigid tank from saturated vapor at 160°C to a final temperature of
400°C. Determine the initial and final pressures, in bar, and sketch the process on T-v and p-v diagrams.
Exercise 14
Steam is contained in a closed rigid container. Initially, the pressure and temperature of the steam are
15 bar and 240°C, respectively. Th
e
temperature drops as a result of heat transfer to the surroundings.
Determine the pressure at which condensation first occurs, in bar, and the fraction of the total mass that
has condensed when the temperature reaches 100°C: What percentage of the volume is occupied by
saturated liquid at the final state?
Exercise 15
The-equilibrium state of a gas are described by a state of the form f(p,v,T)= 0 . In the Amagat's
representation (pv, p), find the slope m of an isotherm in any point of the curve in term of and
+
which are respectively the isothermal compression coefficient of the gas and an ideal gas held in the same
pressure. What conclusion can you give for the regions where m> 0 and the regions where m < 0 ?
Exercise 16
The state equation relative to one mole of a real gas can be represented by an expansion of product pv,
either in term of volume v of gas: pv =
,
-
or in term of pressure pv = A (1 + B' p + C' p
2
+...)
I. For the gas of Van der Waals, expand the product pv with respect to v, then with respect to p in
the second order of Taylor expansion.
2. Deduce the coeffici
e
nts A, B, C, B' and C' in term of temperature
T
and the constants a, b, R of
gas from the Van der Waals equation.
3. Calculate A, B, C, B' and C' for oxygen at the temperature of 25°C, knowing that the experimental
coefficients from Van der Waals equation are a =0.14 , b =3.22 x10
-5
and R= 8.32
www.schoolfaqs.net
