2019-03-01_Physics_Times

(singke) #1
After connecting E, the current through 8 is
1 1
I A E A 8 0 E 4V
2 2

      

After the switch  is closed at t = 0 the inductor
does not allow the current through it and hence
bulb B 2 glows first. After long time the inductor
behaves like a conductor and hence resistance of
the upper wire is less and current through B 1 is
more.

Efficiency,

Output power
Input power



80 200
16
100 4000

s s s
s
p p

V I I
I A
V I



     

Also,

4000
4000 40
p p p 100
V I   I  A

After closing the switch the net potential of the
sphere is zero as it is connected to earth. The
electric field inside the shell is zero (Gauss law)
and hence the potential inside the shell is constant
every where inside the shell and also zero at the
centre.
The net potential at O is

0

(^4040)
o
q q
V
x R
 
Where q is the net charge on the sphere. By
differentiating the equation w.r.t to
0
2
0 0
0
4 4
q dx dq / dt
x dt R

 
0
2
dq Rq dx
.
dt x dt

The current 20
Rq
i v
x

dx dq
v ,i
dt dt
 
   
 
In steady state, the net outward heat flow is
constant, and does not depend on radial position.
Let
2
1 (4 )
dT
c i K r
dr
   
1
4 2
dT c
dr Kr
  

0
1
2 2
1
4
T r
T a
c
dT dr
K r
 


  


1
0

1 1
2
4

c
T T
K r a

 
    
   (1)

When r a   2 T T 0

1
0 0

1 1
2
4 2

c
T T
K a a

    
   (2)
From eq’s (1) & (2) we get

(^40) at 3
3 2
T a
T r
2
1
1
T
T
  
Coefficient of performance
2 2 1
1 2 2 1
/ (1 ) 1
1
1 ( / )
T T T
T T T T
 
     
   
Final pressure in the containers will be the same
0 0
0 0
A B A B
A B
PV PV PV PV
RT RT RT RT
  
(^00)  
(^20000)
A B
P P P P
V V
T T T T
     
(^40)
3
P
 P
For mixture of gases,
(^1122)
1 2
V V
V
n C n C
C
n n



where ,
2
f
C R f is degree of freedom
and
(^1122)
1 2
p p
p
n C n C
C
n n



where
3.Sol:
4.Sol:
5.Sol:
6.Sol:
7.Sol:
8.Sol:
9.Sol:
1
2
p
f
C R
 
  
 
For helium, n 1  4,f 3
For oxygen, 2
1
, 5
2
n  f
5 1 7
(^447)
(^222) 1.62
3 1 5 29
4
2 2 2
p
V
R R
C
C R R
  
   
  

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