R in the equation PV = RT.
Ramsay and Shields suggested that there exists an equation for the surface energy of liquids, analogous to the volume-energy equation of gases, PV = RT.
VPM' to VPM 7, The series of seven pairs of veno-pericardiac muscles (labelled pv in fig.
Pv' to pv 7, The seven veno-pericardiac muscles of the right side (labelled VPM in fig.
VPM' to VPN1 8, The eight pairs of veno-pericardiac muscles (labelled pv in fig.
Q V, or PV = UQ, as in ï¿½ 38 (vi.).
/gr, „Ay,G B; s o T CHunton Boughton Mo chelsea B PV t;y,..,, f,; 'eal?
Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d?
Since dE=dH - pdv, we have evidently for the variation of the total heat from the second expression (8), dF=d(E + pv) =dH+vdp=Sde - (Odv/de - v)dp .
In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv v = constant, which is at once obtained by integrating the equation for the adiabatic elasticity, - v(dp/dv) =yp.
The most natural method of procedure is to observe the deviations from Boyle's law by measuring the changes of pv at various constant temperatures.
It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a function of the temperature only.
But this procedure in itself is not sufficient, because, although it would be highly probable that a gas obeying Boyle's law at all temperatures was practically an ideal gas, it is evident that Boyle's law would be satisfied by any substance having the characteristic equation pv = f (0), where f (0) is any arbitrary function of 0, and that the scale of temperatures given by such a substance would not necessarily coincide with the absolute scale.
If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.
The characteristic equation of the fluid must then be of the form v/0=f(p), where f(p) is any arbitrary function of p. If the fluid is a gas also obeying Boyle's law, pv = f (0), then it must be an ideal gas.
Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =f(p) - SA /30 3, in which f(p) is an arbitrary function of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put f(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .
The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..
We thus obtain E - g o= s 0 (B-o)) - n(pc - poco) (31) We have similarly for the total heat F = E + pv, F - Fo=So(O - oo) - (n+1)(cp - copo)+b(p - p.).
Putting dJ /dm =o at constant volume, we obtain as the condition of equilibrium of the two states J' + p'v' = J" -}- p "v".
In this case dW=pdv=d(pv), a perfect differential, so that the external work done is known from the initial and final states.
In any possible transformation d(D4 - E) cannot be less than d(pv), or the function (E - D4)+pv) =G cannot increase.
The product pv for any state such as D in fig.
- If v is the volume of a homogeneous mass of gas, and N the total number of its molecules, N =v(v+v'+ ...), so that pv =RNT.
Substituting in the momentum equation, we obtain Pv 1 7V + y 2 I V / +PoU 2 I - v) V) = PoU2, whence U 2 = Po (I }-y21 U J .
The term Pv/V added up for a complete wave vanishes, for P/V is constant and Zv=o, since on the whole the compression equals the extension.
The absolute centigrade temperature T is thence inferred from the gas equation (8) R = pv/T = povo/273, which, with p = 2440, v =5, p o = 1, vo =700, makes T =4758, a temperature of 4485° C. or 8105° F.
According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.
Van't Hoff showed that the osmotic pressure P due to a number of dissolved molecules n in a volume V was the same as would be exerted by the same number of gas-molecules at the same temperature in the same volume, or that PV = ROn.
We may observe that the equation (51) is accurately true for an ideal vapour, for which pv = (S-s)0, provided that the total heat is defined as equal to the change of the function (E+pv) between the given limits.
He suggested that the high value for S found by Regnault might be due to the presence of damp in his superheated steam, or, on the other hand, that the assumption that steam at low temperatures followed the law pv = R0 might be erroneous.
PV/6 '=0 .'
R, Constant in gas equation, pv = RU.
Removing the summation signs in equation (52) in order to restrict its application to two points and dividing by the common time interval during which the respective small displacements ds and ds were made, it becomes Pdsfdt = Rds/dt, that is, Pv = Rv, which shows that the force ratio is the inverse of the velocity ratio.