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KVPY SX SB Exam 2016 Question Paper
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© examsnet.com
Question : 25
Total: 120
A container is divided into two equal part I and II by a partition with a small hole of diameter d. The two partitions are filled with same ideal gas, but held at temperature
T
1
= 150 K and
T
2
= 300 K by connecting to heat reservoirs. Let
λ
1
and
λ
2
be the mean free paths of the gas particles in the two parts such that
d
>
>
λ
1
and
d
>
>
λ
2
. Then
λ
1
λ
2
is close to -
0.25
0.5
0.7
1.0
Validate
Solution:
As partition has hole of diameter d, mean pressure between both sections is equal.
∵
Mean force path
(
λ
)
is given by
=
1
√
2
π
r
2
n
v
r
=
radius of the gas particle
n
V
=
number density of gas i.e.
=
N
V
=
(
Total no of particle
)
(
Volume
)
∵
From ideal gas equation
P
V
=
n
R
T
=
N
∕
N
A
R
T
=
N
K
B
T
N
A
=
Avogadro number;
K
B
=
Boltzmann constant
N
A
=
Avogadro number;
K
B
=
Boltzmann constant
⇒
n
y
=
N
V
=
P
k
B
T
∴
λ
=
1
√
2
π
r
2
K
B
T
P
λ
1
λ
2
=
T
1
T
2
×
P
2
P
1
⇒
λ
1
λ
2
=
T
1
T
2
×
√
T
2
√
T
1
λ
1
λ
2
=
√
T
1
T
2
=
√
150
300
=
0.7
© examsnet.com
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