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KEAM 2018 Physics and Chemistry Paper
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© examsnet.com
Question : 36
Total: 120
A cylinder closed at both ends is separated into two equal parts (45 cm each) by a piston impermeable to heat. Both the parts contain the same masses of gas at a temperature of 300K and a pressure of 1 atm. How much the gas should be heated in one part of the cylinder toshift the piston by 5 cm and the pressure of the gas after shifting the piston
T = 365 K and P = 1.125 atm
T = 350 K and P = 1.125 atm
T = 375 K and P = 2.125 atm
T = 350 K and P = 2.125 atm
T = 375 K and P = 1.125 atm
Validate
Solution:
Let the cross sectional area of the cylinder is A.
Initially
Piston is shifted by
5
c
m
in the cylinder
For 1
,
p
1
V
1
T
1
=
p
2
V
2
T
2
⇒
p
V
300
=
p
2
(
V
+
A
x
)
T
2
........(i)
For 2,
p
1
V
1
=
p
2
V
2
⇒
p
V
=
p
2
(
V
−
A
x
)
p
2
=
p
V
(
V
−
A
x
)
....(ii)
From Eqs. (i) and (ii),
p
V
300
=
p
V
(
V
−
A
x
)
⋅
(
V
+
A
x
)
T
2
⇒
T
2
=
V
+
A
x
V
−
A
x
300
=
A
45
+
A
S
A
45
−
A
S
×
300
=
50
40
300
T
2
=
375
K
Putting
T
2
in Eq. (i),
P
2
=
P
V
(
V
+
A
x
)
×
375
300
=
1
×
A
×
45
A
(
450
+
5
)
×
375
300
=
1.125
a
t
m
© examsnet.com
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