Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 19

r----------- cooling - 7

I

I coil in detail I

r- - ------I

I-----

Fig. 1.7.

Solution:

where N is the number of turns, L is the length of the solenoid coil. The

current is therefore

(a) The magnetic field is B = poNI/L,

0.25 x 4
I=----- - = 7960A.
BL
po~ 4T x 10-7 x^100
The total resistance of the coil is R = pL/A. Therefore, the resistance, the
voltage and the power are respectively
(3 X 10-8)(100 X 2~ x 1.5)
R= = 0.0471i-l
(4 x 2 - 2 x 1) x 10-4
V = RI = 375V
P = VI = 2.99 x lo3 kw ,
(b) The rate of flow of the cooling water is W. Then pWCAT = P,
where p is the density, C is the specific heat and AT is the temperature
rise of the water. Hence

2.99 x 103 x 103

P = 17.8 11s

pCAT

w=-=

1 x 4190 x 40

(c) The magnetic pressure is

(0.25)'

= 2.49 x lo4 N/m2.

B2

2po z(4Tx 10-7)

p=-=