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

(^212) Aptitude Test Problems in Physics
The equation of state for n moles of an ideal gas
is p 1 V 1 = nR T 1 , and we can finally write
, 7' 2 , T3 n
A= nR (T 2 — Ti)(— --G).
T1 T2
2.4. Figure 58 shows that on segments 1-2 and
3-4, pressure is directly proportional to tempera-
ture. It follows from the equation of state for an
-ideal gas that the gas volume remains unchanged
in this case, and the gas does no work. Therefore,
we must find the work done only in isobaric pro-
cesses 2-3 and 4-1. The work A 2 3 = p^2 (V^3 — V^2 )
is done on segment 2-3 and A^41 = Pl (V^1 — V^4 )
on segment 4-1. The total work A done by the gas
during a cycle is
A = p 2 (V 3 — V (^2) )P 1 (Vi — V 4 ).
The equation of state for three moles of the
ideal gas can be written as pV = 3R T, and hence
= 3RT 1 , p 1 V 4 = 3RT 4 , p 2 V 2 = 3RT 2 ,
)2 2 V3 = p3 V3 = 3R Ts •
Substituting these values into the expression for
work, we finally obtain
A= 3R (Ti + T3 — T 2 — T 4 )
= 2 x 10 4 I = 20 kJ.
2.5. The cycle 1 --o- 3.-o- 2 -4- 1 is in fact equiv-
alent to two simple cycles 1 0 2 1 and
0 4 3 0 (see Fig. 59). The work done by
the gas is determined by the area of the corre-
sponding cycle on the p-V diagram. In the first
cycle the work is positive, while in the second
cycle it is negative (the work is done on the gas).
The work done in the first cycle can easily be cal-
culated:
A1— (Po—P1) (V2-171)
2 •
As regards the cycle 0 4 -4- 3 •-► 0, the triangle
on the p-V diagram corresponding to it is similar