# P

Mechanics

Oct 27, 2013 (4 years and 6 months ago)

99 views

1.

(a)

Classify the following as closed, open and isolated systems:
-

(i)
Air enclosed in
a rigid wooden chamber

(ii)
Electric Bulb

(iii)
Air Compressor

(iv)
Air enclosed
in a rigid metallic chamber

½ * 4 =
2

(b)

A certain amount of g
as in a
piston
-
cylinder arrangement is expanding at constant temperature.
Consider the gas inside as the system a
nd explain why the system is not in
ther
modynamic
equilibrium.

2

(c)

Classify the following prope
rties as intensive or extensive:
-

(i)

Volume (ii) Density (iii)
Pressure

(iv) Ent
ropy

½ * 4 =
2

(d)

The temperature t on a thermometric scale is defined in terms of a property K by the relation

t = a ln K + b where a and b are constants. The values of K are found to be 1.83 and 6.78 at the ice
point and steam point, the temperatures of which

are assigned the numbers 0 and 100 respectively.
Determine the temperature corresponding to a reading of K equal to 2.42 on the thermometer.

4

2.

(a)

For each of the following systems
,

i
ndicate whether the
energy exchange is
heat
or

work
. Also
indicate whether it is
positive, negative or zero
.

Explain the reasons for
:
-

(i)

A
block of ice at
0
0
C is dropped into water at
45
0
C. Consider
the block of ice

as the system.

(ii)

Atmospheric air
enters
a small, rigid, evacuated bottle. Consider the
air
entering the bottle
as
the system and the bottle
is
well insulated
.

(iii)

Gas
in a

metallic

chamber

is
provided with electrical energy by means of an electric resistance
coil

placed inside
. Consider the gas in

the chamber as the system.

2
*3 = 6

(b)

An electric generator coupled to a windmill produces an average electrical output of 5 kW. The
power is used to charge a storage battery. Heat transferred from the battery to the surroundings
occurs at a constant rate

of 0.6 kW. Determine the total amount of energy stored in the battery in kJ
in 8

h
ours

of operation.

4

3.

(a)

Write the general equation of
the first law of thermodynamics for a
closed
system undergoing a
non
-
cyclic

process
.
Also w
rite the expressions for
various forms of stored energy of a closed
system.

2+2

(b)

What is the difference between heat and internal energy?

2

(c)

Write the steady flow energy equation (SFEE) for
a turbine with negligible heat loss.

2

(d)

Write the energy equation for the filling up
of air into an evacuated bottle which is well insulated.

2

4.

(a)

During one cycle the working fluid in an engine engages in two work interactions: 15 kJ to the fluid
and 44 kJ from the fluid, and three heat interactions, two of which are known: 75 kJ to the f
luid and
40 kJ from the fluid. Evaluate the magnitude and direction of the third heat interaction.

2

(b)

A domestic refrigerator is loaded with food and the door is closed. During a certain period, the
machine consumes 1 kW
-
hr of electricity and the
internal energy of the system drops by 7000 kJ.
Find the net heat transfer for the system.

2

(c)

A gas of mass 1.5 kg undergoes a quasi static expansion which follows a relationship

p

= a + bV

where a and b are constants. The initial and final pressures are 1000 kPa and 200 kPa respectively
and the corresponding volumes are 0.2 m
3

and 1.2 m
3
. The specific internal energy of the gas is
given by the relation
u =
(1.5
pv
)

85
,

kJ/kg
,

where p is i
n kPa and v in m
3
/kg.
Calculate
the net
heat transfer

for the process.

6

5.

(a)

At the inlet to a nozzle, enthalpy of the fluid passing is 3000 kJ/kg and the velocity is 60 m/s. At the
discharge end, the enthalpy is 2672 kJ/kg. The nozzle is
h
orizontal and
there is negligible heat loss
from it. (i) Find the velocity at exit from the nozzle (ii) If the inlet area is 0.1 m
2

and the specific

volume at inlet is 0.187 m
3
/kg, find the mass flow rate

5

(b)

A rigid tank of volume 0.5 m
3

is initially evacuated. A tiny hole develops in the wall, and the air
from the surroundings at 100 kPa, 21°C leaks in. Eventually, the pressure in the tank reaches 100
kPa. The process occurs slowly enough that heat transfer between the tank and the surro
undings
keeps the temperature of the air inside the tank constant at 21°C. Determine the amount of heat
transfer from the tank. Assume for air, C
p

= 1005 J/kg K, C
v

= 718 J/kgK, R = 287 J/kgK

5

PES Institute of Technology, Bangalore

(Autonomous Institute under VTU, Belgaum)

ME2
08

CONTINUOUS INTERNAL EVALUATION (CIE)
3
rd

BE
September

2011

FIRST
TEST

ME
208
:
ENGINEERING THERMODYNAMICS
Duration: 90 Minutes

Answer All Questions Max Marks: 50

USN

SOLUTIONS TO NUMERICALS

1(d)
The

temperature t on a thermometric scale is defined in terms of a property
K by the relation t = a ln K + b

w
here a and b are constants.

The values of K are
found to be 1.83 and 6.78 at the ice point and steam point, the temperatures of
which are assigned th
e numbers 0 and 100 respectively. Determine the
temperature corresponding to a reading of K equal to 2.42 on the thermometer.

Solution
:

At ice point, t = 0. K = 1.83

t = a ln K + b gives us:

0 = a (0.6043) + b

Hence, b =
-
0.6043a.

At steam point, t
= 100, K = 6.78.

100 = a (1.9139)
-

0.6043a (borrowing the value of b as
-
0.6043a).

Or a = 75.35.

And hence b =
-
0.6043 x 75.36 =
-
45.53.

When K = 2.42, t = 75.36 (ln 2.42)

45.53.

=21.3°C

2 (b)
An

electric generator coupled to a windmill produces an average electrical
output of 5 kW. The power is used to charge a storage battery. Heat transferred
from the battery to the surroundings occurs at a constant rate of 0.6 kW.
Determine the total amount of

energy stored in the battery in kJ in 8h of
operation.

Solution:

8 hours = 28800 seconds.

The battery gets charged at a rate of 5 kW but loses power at a rate of 0.6 kW.

Net rate of charging = 5

0.6kW = 4.4 kW

Total energy stored = Power x Time = 4.4

x 28800 = 126720 kJ.

4(a)
During one cycle, the working fluid of an engine engages in two work
interactions : 15 kJ to the fluid and 44 kJ from the fluid, and three heat
interactions, two of which are known : 75 kJ to the fluid and 40 kJ from the
flui
d. Evaluate the magnitude and direction of the third heat transfer.

Solution:

∂Q = ∂W for a cyclic process

Hence, +75

40 + Q = 44

15

Giving : Q =
-
6 kJ.

4 (b)
A

domestic refrigerator is loaded with food and the door is closed. During a
certain period, the machine consumes 1 kW h of energy and the internal

energy
of the system drops by 7
000 kJ. Find the net heat transfer for the system.

Solution:

∂Q = ∂W + ΔE

Wor
k done by the system is negative, also is the change in internal energy.

Hence, ∂Q =
-
10
.6 MJ.

4 (c)
A gas of mass 1.5 kg undergoes a quasi static expansion which follows a
relationship
p

= a + bV
where a and b are constants.

The initial and final
pressures are 1000 kPa and 200 kPa respectively and the corresponding volumes
are 0.2 m
3

and 1.2 m
3
. The specific internal energy of the gas is given by the
relation

u = 1.5 pv

85 kJ/kg
where p is in kPa and v in m
3
/kg.
Calculate
th
e net
heat transfer and the maximum internal energy of the gas attained during the
expansion.

Solution:

p = a + bV

Taking p
1

= 1000 kPa
p
2

= 200 kPa

V
1

= 0.2 m
3

V
2

= 1.2 m
3

We obtain two equations in ‘a’ and ‘b’, and hence we can solve for t
hem.

b =
-
800000 Pa/m
3

a = 1160000 Pa

Work done is ∫PdV

(lower limit = 0.2m
3

upper limit = 1.2m
3
)

a(V
2

V
1
) +

(V
2
2
-
V
1
2
)

= 600000 J

u = 1.5 pv

85, multiplying by mass.

U = 1.5pV

127.5 kJ

U
1

= 172.5 kJ

U
2

= 232.5 kJ

ΔU = ΔE = 60 kJ

Q = W + ΔE

= 600 kJ + 60 kJ = 660 kJ.

5 (a)
At the inlet to a nozzle, enthalpy of the fluid passing is 3000 kJ/kg and the
velocity is 60 m/s. At the discharge end, the enthalpy is 2672 kJ/kg. The nozzle is
horizontal and there is negligible heat loss from it.
(i
)

Find the velocity at exit
from the nozzle.

(ii) If the inlet area is 0.1 m
2

and the specific

volume at inlet is
0.187 m
3
/kg, find the mass flow rate.

Solution:

Energy in = Energy out

h
1

+ V
1
2
/2 = h
2

+ V
2
2
/2

(‘h’ denotes enthalpy and ‘V’ velocity,
sub
scripts refer to entry and exit)

Knowing all values but V
2
, we determine its value to be 692.6 m/s

̇

A
1
V
1
/s
1

(s denotes specific volume)

From which we can obtain

̇

as 32.08 kg/s

5 (b)
A rigid tank of volume 0.5 m
3

is initially evacuated. A tiny
hole develops in
the wall, and the air from the surroundings at 1 bar, 21°C leaks in. Eventually,
the pressure in the tank reaches 1 bar. The process occurs slowly enough that
heat transfer between the tank and the surroundings keeps the temperature of
the

air inside the tank constant at 21°C. Determine the amount of heat transfer.

Solution:

For air, c
p

= 1005 J/kg K. c
v

= 718 J/kgK. R = 287 J/kgK

m
in
E
in

+ Q
in

= m
sys
E
sys

(m
sys

= m
in

= p
sys
V
sys
/RT
sys

= 0.59 kg)

0.59 (c
p
T
in
) + Q
in

= 0.59(c
v
T
sys
)

Giving

Q
in

=

-

50 kJ