An equation is derived relating the internal pressure of a rubber balloon to its radius. The theoretical pressure curve is shown to be experimentally verifiable in the case of low to moderate extensions, as long as the effects of hysteresis are ignored. The problem of the equilibrium configuration of two interconnected balloons is also discussed.
A description is given of the equilibrium states of a system composed of two spherical membranes made of either soap film or rubber. The membranes are filled separately with air to unequal radii and then connected by a hollow tube, allowing the air to pass freely from one to the other. The equilibrium configurations are determined by the method of minimization of the availability of the system at constant temperature.
We present a study of the orientational order parameter a. for D2 molecules with both rotational angular momentum J=1 (para-D2) and J=O (ortho-D2) in the ordered cubic phase. Our study covers the temperature range between 0.4 and 4 K at mole fractions X of (J=1) molecules 0.55 «X~0.96. The order parameters 0~+.~&(T, X) and cr(z.o&(T, X) are proportional to the respective doublet splitting observed in the NMR spectrum. In the ordered phase, two doublets spaced symmetrically around the central Larmor frequency are recorded. The outer one, with a splitting g v~q .~& up to about 78 kHz, represents the signal from the (J = 1) molecules. The inner one, with splitting pv(J ()& an order of magnitude smaller than pv(z.~&, is caused by polarization of the (J=O) molecules by the (J=1) field. A description is presented of the line shape as a function of T and X. Using the results from several samples, we obtain the extrapolated (J =1) order parameter for X=1 as a function of T. At the orderdisorder transition temperature T&, the doublet structure suddenly disappears and is replaced by a sharp central line which is characteristic of the orientationally disorderedphase. The first-order nature of the transition is thus clearly shown. The experimental order parameter for (J=1) molecules 0.~& .~& (X=1, T) is compared with predictions from a meanfield and a cluster-variation theory, and also with results from Raman spectroscopy. As X decreases, the line structure shows a progressively greater temperature variation and becomes more smeared out as the order-disorder transition is approached. Below a critical mole fraction X~=0. 54, obtained by extrapolation, no doublet structure is observed. The limiting value of both 0 (J.~& and 0. &J.O& as a function of X at T «T&, (X) is in good agreement with predictions by Harris. A fit of the experiment to theory leads to a factor of about 0.02 for the reduction of the order parameter by the zero-point motion, in agreement with theoretical predictions. It is also shown that, within experimental error, the temperature variation of both order parameters 0(z.&& and 0. (& 0& for a given X is the same. We briefly discuss the failure to observe the doublet splitting for the NMR pair spectrum of two neighboring (J=1) molecules in an hcp D2 sample with X=0.05, and mention other peculiarities that at this time remain unexplained for dilute mixtures of (J=1) molecules in (J =0) D2. The possible existence of a large crystalline field that might account for these anomalies is suggested.
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