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JEE Advanced 2015 Paper 2
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© examsnet.com
Question : 15
Total: 60
An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston(as shown in figure).Initially the gas at temperature
T
1
pressure
P
1
and volume
V
1
and the spring is in its relaxed state the gas is then heated very slowly to temperature
T
2
,pressure
P
2
and volume
V
2
.During process the piston moves out by a distance x.Ignoring the friction between the piston and the cylinder the correct statement(s) is (are)
[JEE Adv 2015 P2]
If
V
2
=
2
V
1
‌
and
‌
T
2
=
3
T
1
,then the energy stored in the spring is
1
4
P
1
V
1
If
V
2
=
2
V
1
‌
and
‌
T
2
=
3
T
1
,then the charge in internal energy is
3
P
1
V
1
If
V
2
=
3
V
1
‌
and
‌
T
2
=
4
T
1
,then the work done by the gas is
7
3
P
1
V
1
If
V
2
=
3
V
1
‌
and
‌
T
2
=
4
T
1
,then the heat supplied to the gas is is
17
6
P
1
V
1
Validate
Solution:
B or A,B,C
P(pressure of gas)=
P
1
+
k
x
A
W
=
∫
P
d
V
=
P
1
(
V
2
−
V
1
)
+
k
x
2
2
=
P
1
(
V
2
−
V
1
)
+
(
P
2
−
P
1
)
(
V
2
−
V
1
)
2
Δ
U
=
n
C
v
Δ
T
=
3
2
(
P
2
V
2
−
P
1
V
1
)
Q=W+ ΔU
Case 1: ΔU
=
3
P
1
V
1
,
W
=
5
P
1
V
1
4
,
Q
=
17
P
1
V
1
4
,
U
s
p
r
i
n
g
=
P
1
V
1
4
Case 2: ΔU
=
9
P
1
V
1
2
,
W
=
7
P
1
V
1
3
,
Q
=
41
P
1
V
1
6
,
U
s
p
r
i
n
g
=
P
1
V
1
3
Note:
A and c will be true after assuming pressure to the right of piston has constant value of
P
1
© examsnet.com
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