WATER 
is determined from the empirical values of B(t), 
fitting the original isothermal Tait equation, Eq. 
(2.7), to experimental data. R. E. Gibson™ gives 
third-degree t-expansions of B(t) for various 
molalities of NaCl. By interpolating the coef- 
ficients (the constant term numerically and the 
other graphically) for a molality of 0.7, one 
obtains B(t)=3.134—1.65 X10-4(t—55) —1.181 
X 10-4(¢—55)?+5.32 X 10-7(t—55)8 kilobars. 
The specific heat c,(0, 7) for a 0.7 molal NaCl 
solution was obtained by interpolation from the 
values quoted in the International Critical Tables 
and Physikalischchemtische Tabellen. The resulting 
set of values is fitted adequately by the ex- 
pression 
c,(0, £+273.16) =3.9644-+4 6.24 
X 10~4t joule/gm. deg. 
From Gibson and Loeffler“ a set of values of 
v(0, 7) covering the range from 25°C to 95°C 
inclusive was obtained for a 0.7 molal NaCl 
solution by means of empirical equations giving 
v(0, 7) as a function of concentration for each 
temperature. In extrapolating to higher tem- 
peratures, the relation, 
v(0, £273.16) =0.994150+ 2.929 x 10-4(t— 25) 
+3.241 x 10-§(t— 25)? cm3/gm. 
was used ; for lower temperatures (¢<10°C), 
v(0, £+273.16) =0.991442 + 6.025 
X 10-*(t— 3.8)? cem3/gm. 
2. Test of the Modified Tait Equation with 
Bridgman’s Data for Pure Water. Deter- 
mination of the Characteristic 
Constant n. 
The modified Tait equation-of-state, Eq. 
(2.12), may for our present purposes be written 
in the form 
log(2L0, SJ/vLp, SJ) 
=(1/n) log(1+p/A[S])  (II-1) 
where A[.S] is related to the B(t) in the original 
isothermal equation of state as follows, 
A[S]=B(to), 
to= T»—273.16, (II-2) 
T,=T[0, S]. 
13 Private communication. 
M4 Gibson and Loeffler, J. Am. Chem. Soc. 53, 443 (1941). 
AD DE PRONT OF A SHOCK WAVE 
381 
793 
According to the convention introduced in Part 
B of Section II, parentheses ( ) after a function 
denotes that the independent variables are p and 
T, whereas square brackets [ ] denote that they 
are p and S. 
Now we wish to test Eq. (II-1) with Bridg- 
man’s!® p-v-T data for pure water with the 
ultimate object of finding the best value for n. 
We assume implicitly that 2 does not vary 
rapidly with NaCl concentration. To make the 
comparison, we first must know the values of the 
temperature JZ corresponding to the various 
points [p, S], the calculation of which we con- 
sider below. 
Letting 70, SJ=To, Tip, S]=T, and F—TLo 
= AT, we have 
> aT[p, S > ofp, S 
cal aes “p= f == Jip. (11-3) 
0 Pp 0 
Using Eq. (II-1), a simple calculation yields 
me WiLalg/Ayuas +D)(1+p/A) 
—(n+D)(1+p/A)""-+-n—1], (I-A) 
where 
A=A[S]=B(éo), 
po S] ic TB’ (to) -v(0, To) 
n—1 (1—1)-c,(0, To) 
dvL0, S] 
aS mB(te)Bo 
A'TSWLO, S]  B’(to)0(0, Ta)’ 
av(0, ~) 
out T= 1p 
’ 
nALS | 
o= 
To calculate T, given a specified p and 
T)=T7[0, S], a tentative value of 2=7.15 was 
chosen for use in Eq. (II-4). The corresponding 
value of vl p, S]=v(p, T) was obtained by inter- 
polation from Bridgman’s'® p-v-T data. In- 
serting these values of o[ p, S] in Eq. (II-1), and 
knowing the values of v[0,S]=v(0, 7c) and 
B(to) for pure water, a set of values of ” was 
calculated for p=5,000, 15,000, 25,000 kg/cm? 
1s Bridgman, J. Chem. Phys. 3, 597 (1935) and private 
communication. 
