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JEE Mains Model Paper 12
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© examsnet.com
Question : 55
Total: 90
A resistance coil of resistance 7.5 W, connected to an external battery, is placed inside the thermally insulating smooth piston and containing an ideal monoatomic gas.
A current of 2 A is passed through the coil such that it is generating heat at a constant rate inside the cylinder. Volume of the chamber of the cylinder is 5
m
3
and area of the piston is 0.1
m
2
. The mass rate of dropping sand on the piston such that the piston always remains stationary will be … (Assuming that the sand is dropped very swiftly and g = 10
m
s
−
2
)
0.01
K
g
s
−
1
0.02
K
g
s
−
1
0.03
K
g
s
−
1
0.04
K
g
s
−
1
Validate
Solution:
Rate of heat generation, H =
i
2
R
=
2
⋁
2
× 7.5 = 30
J
s
−
1
As volume of the gas is constant, heat given = change in internal energy
Hdt = n
C
v
dT ⇒
d
T
d
t
=
H
n
C
v
... (i)
From ideal gas equation PV = nRT, on differentiating at constant volume, we get
VdP = nRdT ⇒
d
T
d
t
=
V
n
R
d
P
d
t
... (ii)
From (i) and (ii), we get
V
n
R
d
P
d
t
=
H
R
V
C
v
⇒
d
d
t
(
m
g
A
)
=
H
R
V
(
3
R
∕
2
)
⇒
g
A
d
m
d
t
=
2
H
3
V
⇒
d
m
d
t
=
2
H
A
3
g
V
=
3
×
30
×
0.1
3
×
10
×
5
= 0.04
k
g
s
−
1
© examsnet.com
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