# Tutorial sheet no. 1

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29 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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Tutorial sheet no. 1

1
. The pressure volume correlation for a quasi
-
static process is given by:

P= (8
-
4V) bar, where V is in meter
-
cube. Determine the work done when volume changes from 0.60

m
3
to 0.35 meter
-
cube.

2. The properties of cl
osed system change following the relation b/w pressure and volume as:

P*V=3.0 where p is in bar, V is in m
3
. Calculate work done when pressure increases from 1.5

bar to 7.5 bar.

3. The work
-
supplied to closed syst
em is 160 kJ
. The initia
l volume is 0.80 m
-
cube
a
n
d

pressure of the

system changes as p= (7
-
3V) where p is in bar, V is in m
3
. Determine the final volume and

pressure of the system.

4. A spherical balloon of 1
-
m diameter contains a gas at 220 kPa and 320 K. the ga
s inside the balloon

is heated until the pressure reaches 550 kPa. During the process of heating pressure of the gas is

proportional the diameter of the balloon. Calculate the work
-
done by the gas inside the balloon.

5. A fluid at a pressu
re of 3 bar, and with a specific volume of 0.18 m
3
/kg, contained in a cylinder

behind a piston expands reversible to a pressure of 0.6 bar acc to the law p
-
C/v
2

where C is

constant. Calculate the work
-
done by the fluid on the piston.

6.
Convert

the following readings of pressure to kPa assuming that barometer reads 760mm of mercury.

i) 80cm of Hg.

ii) 1.35m H
2
O
gauge

iii) 30 cm of Hg vacuum.

iv) 4.2 bar.

7. 1.7 example of R.K. Rajput page 29

Tutorial sheet no. 2

1.

1.5kg nitrogen con
tained in a cylinder at a pressure 6
bar

and temp 300k expands
three times

its
original volume. Assuming the expansion process to be isobaric make calculations for:
-

(a)

initial volume

(b)

final temperature

(c)

work done by gas

(d)

(e)

change in internal energy

2.

100

liters

of hydrogen gas at 300k temp. and 5 bar pressure is contained in a cylinder fitted with a
frictionless piston. The piston carries some dead weight, can move freely and its upper part is
exposed to atm. Pressure. There is input of paddle work to the

gas and its temp. rises to 350k.
determine:
-

(a)

work done

(b)

change in internal energy

(c)

change in enthalpy

(d)

3.

air initially at 60kPa pressure 800k temp and occupy a volume of 0.1m
3

is compressed
isothermally until the volume is half and subsequently it

goes further compressed at constant
pressure till the volume half again. Sketch the process on pv plot and make calculations for total
work done and total heat interaction for two process.

4.

2kg of an ideal gas is compressed adiabatically from pressure 100k
Pa and temp 220k to final
pressure 400kPa. Assuming the expansion process to be isobaric make calculations for:
-

(a)

final volume

(b)

work done by gas

(c)

(d)

change in internal energy

5.

3kg of an ideal gas is compressed
polytropically from

pressure 1
00kPa and temp 300k to final
temp500k , pressure 1500kPa..make calculations for:
-

(a)

index polytropic

(b)

final volume

(c)

work of compression

(d)

6.

a vertical cylinder 0.20m bore has its piston initially 0.30m above bottom position consists Co2.
Th
e piston is loaded with 1000N weight and pressure 1 bar and 293 k temp . the gas is heated
with a heater of 1 Watt for an hour. There is no heat loss to the surroundings. Find piston lift.
(Cp=0.82kJ/kg
-
k,R=189J/kg
-
k)
.

7.

Tutorial sheet no. 3

1.

A nozzle

2
, specific volume 142litres/kg, internal energy 4400kj/kg
and negligible speed. At the outlet, the pressure is 100kN/ m
2
, specific volume 1660 litters/kg and
internal energy 2200kj/kg. calculate:
-

(a)C2

Neglect heat loss and assu
me the nozzle to be horizontal.

2.

In an isentropic flow through nozzle, air flows at the rate of 600kg/h. at inlet to the nozzle,
pressure is 2MPa and temp is 127
o
C. The exits pressure is 0.5MPa, inlet velocity is 300m/s.
Determine:
-

(a) Velocity at outlet

3.

A

steam turbine operates under steady flow condition receiving steam at the following state:
-

h
1
=2785kJ/kg C
1
=33.3m/s h
2
= 2512kJ/kg C
2
=100m/s

T
he intake is 3m above the exhaust, the tu
rbine develop 112.5kw. The heat loss to the

Surroundings is at the rate of 0.29kJ/s. determine the steam flow rate through turbine.

4.

For centrifugal compressor , properties of the air at inlet and outlet are listed below:
-

P
1
=1bar, P
2
= 5.5 bar v
1
=0.77m
3
/kg v
2
= 0.20m
3
/kg C
1
= 12m/s C
2
= 90m/s

Air flow rate at inlet is 15m
3
/min. the compressor is driven by 40kw motor and heat lost to the
surroundings is 30kJ/kg, Neglecting changes in poten
tial energy. Calculate du

5. A centrifugal pump delivers 50 kg of water per second. The inlet and outlet pressures are 1 bar and
4.2 bar respectively. The suction is 2.2m below the center of the pump and delivery
is 8.5m above the
center of the pump.

The suction and delivery pipe diameters are 20cm and 10cm respectively. Determine
the capacity of the pump.

Tutorial sheet no.4

1.

a heat pump is used to heat the house in winter.396421 kj/h of heat is to be supplied
to the house and for operating the hea
t pump,29874 kj/h of work is required. Find out
the C.O.P.of the heat pumped quantity of heat it extracted from the outside air. If heat
pump is reversed i.e. it is used for cooling the house by rejecting the heat to the
outside air is 396421kj/h then what

will be the COP of the pump.

2.

An engine working on a Carnot cycle receives 1020kj heat from a heat reservoir at a
constant temperature of 950
0
C and rejects heat to a heat sink at a constant
temperature of 30
0
C.calculate:i) the thermal efficiency of the en
gine. Ii) The work
done.

3.

A reversible engine with 40% efficiency discharges 1520KJ of heat per minute at
27
0
C to a pond. Find the temperature of the source which supplies the heat to the
engine and power developed by the engine.

4.

Source S1 can supply energy

at the rate of 12500 KJ/min at 317
0
C. A source S2 can
supply energy at the rate of 125000KJ/min at 77
0
C.Which source would you choose
to supply energy to an ideal reversible heat engine that is to produce a large amount
of power if temperature of surround
ings is 37
0
C?

5.

Two Carnot engines work in series between the source and the sink temperature of
600K and 400K.if both the engines develop equal powers determine the intermediate
temperature.

Tutorial sheet no. 5

1.

A rigid cylinder containing 0.00
5 m
3

of nitrogen (molecular mass 28) at 1 bar 290 K is
heated reversibly unti
l the temperature becomes 360 K. determine the heat supplied and
entropy change ν=1.4.

2.

4m
3

of air at pressure of 500kPa and temperature of 27
0
C expand reversibly in a cylinder
to a pressure of 100kPa.The final volume is 20m
3
. Assume constant specific heat
for this
and calculate 1) heat transferred during the process.2) the change of entropy during the
process.

3.

5kg of air is compressed in a reversible steady flow polytropic process from 100 kPa. and
40
0
C to 1000kPa and during this process the law followed by

the gas is pV
1.25
=C.
determine the shaft work, heat transferred and the change in entropy Cv=0.717kJ/kg,
R=.287kJ/kg.

4.

A Carnot heat engine draws heat from a reservoir at temperatureT1 and rejects heat at
temperature T
3
. This engine drives a Carnot refrige
rator which absorbs heat from a
reservoir at temperature atT2 and rejects heat to a reservoir at temperature T
3

if T1=600K
and T
2
=300K Determine

a) the temperature T such that the heat supplied to the engine Q1 is equal to the heat
absorbed by the refrigeratorQ2.) The efficiency of Carnot cycle and C.O.P. of Carnot
refrigerator.

5. A reversible engine working in a cycle take
s 4500 kJ of heat from a source at 750K per
minute and develops a power of 15kw. The engine rejects heat to two reservoirs at 300K
and 400K. Determine the thermal efficiency and heat rejected to each sink.

6. 1 kg of air at 1bar and 300k is compressed

adiabatically till its pressure becomes 5 times
the original pressure. Then it is expended at constant pressure and finally cooled at

1) Heat transfer

2) Internal e
nergy

Represent on PV and T
-
S chart

C
v

=
-

1.8 kj/kgk
ν
= 1.4

Tutorial sheet no. 6

1.

The peak pressure in an O
tto cycle is 21 bar. with a compression ratio of 5 and
minimum pressure of 1 bar determine a)thermal efficiency)mean effective pressure.
Assume the working substance as air with
ν=1.4.

2.

An air engine working on Otto cycle has compression ratio raised from 5

to
6.compare the change in efficiency due to this rise.
ν=1.4.

3.

An engine working on the dual cycle has cylinder bore of 20 cm and stroke 40cm.The
compression ratio is 14.5 and the pressure ratio of constant volume heat addition is
1.5.the constant pressur
-
off takes place at 4.9% of the stroke.
Determine the air standard efficiency.

4.

An air standard diesel cycle has compression ratio of 14.The pressure at the beginning
of the compression stroke is 1 bar and temperature 27
0
C.The maximum tem
perature
of the cycle is2500
0
C.Determine the thermal efficiency of the engine.

5.

The mean effective pressure of an ideal diesel cycle is 7.5 bar. If the initial pressure is
1 bar and the compression ratio is 12.5, determine the constant pressure cut
-
off rati
o
ν=1.4.

6.

In an engine working on diesel cycle the following data was obtained temperature at
0
C.temperature at the end of constant
pressure process=1600
0
C.compression ratio=1.4.Cp=.24kJ/kgK and Cv=.17kJ/kgK.
Calcula
te

i)

The temperature at the end of adiabatic compression.

ii) The percentage of stroke at which the cut
-
off occurs.

Iii) The temperature at the end of adiabatic expansion.

IV) The air standard efficiency.

7.

The swept volume of a diesel engine working on a dual

cycle is 0.0147m
3

and
clearance volume is0.0018m
3
. The maximum pressure is 60 bar. Fuel injection ends at
4% of the stroke. The pressure at the start of the compression is 1 bar. Determine the
air standard efficiency.

8.

An isentropic air turbine is used to
supply 0.15kg/s of air at 0.1MN/m
2

and at 280K to
a cabin. The pressure at the inlet of the turbine is 0.4MN/m
2
.Determine the
temperature at inlet and power developed by the turbine Cp=10.kJ/kg K.

Tutorial sheet no. 7

1. A mild steel rod 20mm in d
iameter is subjected to an axial pull of 50kN. Determine the tensile
stress induced in the rod and the elongation if unloaded length is 5m. E=210GN/m
2
.

5. A steel rod 15m long is at a temperature of 15
0
C. Find the free expansion of the length when
the temperature is raised to 65
0
C. find the temperature stress produced when

i.

The expansion of the rod is prevented

ii.

The rod is permitted to expand by 6mm.

2. A steel wire 2m long and 3mm in diameter is extended

by 0.75mm due to weight suspended
from the wire. If the same weight is suspended from a brass wire, 2.5m long and 2mm diameter,
it is elongated by 4.65mm. Determine the modulus of elasticity of brass if that of steel is
2x10
5
N/mm
2
.

3. A steel bar for cent
imeter in section , 3mm long is subjected to an axial pull of 128 kn. Taking
E = 200 GN/m square . Calculate the alternation in the length of the bar. Calculate also the
amount of energy stored in the bar during extension.

4. The following observations we
re made during a tensile test on a mild steel specimen 40mm in
diameter and 200mm long.

Elongation with 40kN load is 0.0304mm

Length of specimen at fracture=249mm

Determine:

a)

Young’s modulus of elasticity

b)

Yield point stre
ss

c)

Ultimate stress

d)

Percentage elongation

5. a steel tie rod 50mm dia. And 2.5m long is subjected to a pull of 100kN to what length the rod
should bored centrally so that the total extension will increase by 50% under the same pull, the
bore being 25mm dia.
?Take E=200GN/m
2