60 Aptitude Test Problems in Physics
2.17. A space object has the shape of a
sphere of radius R. Heat sources ensuring
the heat evolution at a constant rate are
distributed uniformly over its volume. The
amount of heat liberated by a unit surface
area is proportional to the fourth power of
thermodynamic temperature.
In what proportion would the tempera-ture of the object change if its radius de-
creased by half?
2.18*. A heat exchanger of length 1 con-
sists of a tube of cross-sectional area 2S
with another tube of cross-sectional area
ri
rf
(^) I $
tt
Tr (^2) V
`N
c") it
l
o) ri^2
Fig. 65
S passing through it (Fig. 65). The walls of
the tubes are thin. The entire system is ther-
mally insulated from the ambient. A liq-
uid of density p and specific heat c is pumped
at a velocity v through the tubes. The
initial temperatures of the liquid in the
heat exchanger are T 11 and T 12 respec-
tively.
Determine the final temperatures Tf1
and Tf 2 of the liquid in the heat exchanger