217 
Sec. 4 -6- el4 Wjaa5 
situation is shown in Fig. 4-1 in which the ordinate represents distance 
alongs the tube and the abscissa represents the time. The full line gives 
the yosition of the piston as a function of the time, while the dashed line 
shows the progress of the shock wave initiated by the sudden acceleration of 
the piston. 
D 
/ Po, Vo, Ww 
Fig. 4-1 
The region in front of the gas is at rest with pressure Pj and snecific 
volume Vi: The as behind the shock wave is at the higher pressure Pp, 
lower specific volume Vp (higher density), and is moving with the uniform 
velocity w, that of the piston, The values of Pp, Vo, w, Py and Vj are con~ 
nected by the three basic equations of Sec. 3. The motion of the gas on 
other side of the shock wave must satisfy the differential equations of Sec. 2. 
Obviously, a mass of gas of uniform density and pressure moving at a uniform 
velocity does satisfy these equations. The three equations at the discon- 
tinuous shock front are just sufficient to svecify the unknowns D, Po and Vo 
in terms of the piston velocity w. 
b. Application te an ideal gas.* If the heat camacity is assumed to 
be constant, the energy of a verfect sas is 
B= Gy i=rey) (5 EP Ty), (13 )* 
where c, is the specific heat at constant volume and T the absolute 
Vv 
temperature. Insertion of this and the equation of state 
PV = Ri/M 
(R is gas constant per mole and M the molecular weight) into the basic 
equations of Sec. 3 leads to the following results. 
]H + Vie pu? t (14) 
D 
~——— 
/ 
he He + ee (15)* 
(l+ ¥ )w/ta , y = 1/4 (L+ ow | 
V ver, /t 25 a 
* Nquations valid for ideal gases only will be marked with the symbol *, 
where KB 
and a 
