Consider a spherical cryogenic reservoir containing a liquid refrigerant at $-10C($as shown in the

figure$).$ The reservoir has two metal walls of negligible thickness $($inner wall radius: $R_1=1m)$

with the space between walls, with $1cm$ thick, filled with air at $0\mathrm{.}1$atm. The surface of the outer

metal wall also has an insulating material coating with $1cm$ thick. Knowing that the temperature

of the internal metal wall $(T_1)$ is $-5C,$ that the temperature of the external metal wall $(T_2)$ is $5C$

and that the reservoir is surrounded by air at $25C$ :

a$)(20\%)$ Represent the thermal circuit that describes the heat transfer mechanism between the

air outside and the fluid inside the reservoir.

b$)(10\%)$ Calculate the heat transfer rate.

c$)(10\%)$ How would change the heat transfer rate calculated in point b$)$ if the space between

the metal walls of the reservoir was under vacuum $(P=0)?$ Justify conveniently.

Please solve it with answers and all steps. Thank you.