Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

216 Aptitude Test Problems in Physics

for CO 2 , we find that the velocity of the descent

module of the spacecraft is

RT Ap

vr-- --

P At

8.3 J/ (K • mol) X 7x 10 2 K

10 m/s 2 x 44 x10-3 kg/mol x 1150 s

11.5 m/s.

Let us now solve the second part of the prob-

lem. Considering that the module has a velocity

of 11.5 m/s, it was at an altitude h = 15 km above

the surface of the planet 1300 s before landing,

i.e. this moment corresponds to t = 2350 s. Using

the relation (Ap/At) p-1, we can find the required

temperature Th at this point of the graph from

Eq. (2):

Th=

mu, p At

t

430 K.

R k Ap

2.9. Since the piston has been displaced by h under

the action of the load, the volume of the gas has

decreased by hS and has become V — hS. The gas

pressure under the piston is equal to the atmospheric

pressure Po plus the pressure Mg/S produced by the

load, i.e. Po Mg/S. Therefore, we can write

the equation of state for the gas before and after

loading:

poV = nRTI, (1)

po + MgIS

—nRT f. (2)

V —hS

Here T 1 and Tf are the initial and final tempera-
tures of the gas.
Since the gas is thermally insulated by hypoth-
esis, it follows from the first law of thermody-
namics that the entire work A done on the gas is
spent to change its internal energy. i.e. A =
(3/2)nR (Ti — Ti) (the internal energy of a mole
of an ideal gas is U = (3/2)RT). It can easily