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WBJEE 2014 Physics Solved Paper
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© examsnet.com
Question : 59
Total: 60
A heating element of resistance r is fitted inside an adiabatic cylinder which carries a frictionless piston of mass mand cross-section A as shown in diagram. The cylinder contains one mole of an ideal diatomic gas. The current flowsthrough the element such tha the temp rature rises with time t as ΔT = αt +
β
t
2
(α and β are constants), whilepressure remains constan The atmospheric pressure above the piston is
P
0
. Then
the rate of increase in internal energy is
5
2
R (α + βt)
the current flowing in the element is
√
5
2
r
R
(
α
+
β
t
)
the piston moves upwards with constant acceleration
the piston moves upwards with constant speed
Validate
Solution:
Internal energy U =
n
f
R
T
2
U =
5
R
2
[
α
t
+
1
2
β
t
2
]
d
U
d
t
=
5
R
2
[
α
+
β
t
]
dQ = n
C
p
dT ,
d
Q
d
t
= n
C
p
×
d
T
d
t
i
2
r
=
7
2
R
× [α + βt]
i =
√
7
2
r
R
(
α
+
β
t
)
, PV = nRT
V =
n
R
T
P
V =
n
R
P
[
α
t
+
1
2
β
t
2
]
x =
n
R
P
A
[
α
t
+
1
2
β
t
2
]
, v =
n
R
P
A
[α + βt]
acceleration =
n
R
P
A
× β
© examsnet.com
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