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Similarly at B-c interface,
CB
dx
dT
dx
dT
((k
B
>k
C
)
When
dx
dT
constant, T(x) is linear
When
dx
dT
linear, T(x) is quadratic
Hence the correct temperature distribution is
T
x
Two mark
1. A rigid vessel of volume 10m
2
is filled with hydrogen at 35C and 500 kPa. Due to
leakage, some gas has escaped from the vessel until the pressure in the vessel drops
down to 200 kPa, and the corresponding temperature of the gas inside the vessel is found
to be 25C. The amount gas leaked (in kg) from the vessel is___
Ans: 2.291 (range 2.2 to 2.5)
Sol: P
1
=500 kPa
V
1
=10m
3
T
1
= 273+35=308 K
157.4
2
314.8
M
R
R
2
2
H
H
11
1
1
500 10
3.905
4.157 308
PV
m kg
RT
P
2
= 200 kPa (final state)
V
2
= 10m
3
(rigid vessel)
T
2
= 273+25=298K
22
2
2
200 10
1.614
4.157 298
PV
m kg
RT
Amount gas leaked = m
1
m
2
= 3.9051.614=2.291kg
2. An air standard diesel engine has a compression ratio of 18 (the ratio of the volume at
the beginning of the compression process to that the end of the compression process),
and a cut off ratio of 3 (the ratio of the volume at the end of the heat addition process to
that at the beginning of the heat addition process). The thermal efficiency (in%) of the
engine is______
Ans: 59 (range 57 to 61)
Sol: r
k
= 18
r
c
= 3
1r
1r
r
1
1
2
y
c
1y
k
th
0.4
1 4.65 1
1
1.4 18 3 1





=0.589=59%