The Effect of Confinement on Liquid Helium Near the Lambda Line

This thesis is the compilation of several projects relevant to the behavior of confined liquid helium near the lambda-line. The first project described is the development of two new high resolution thermometers optimized for specific heat studies of helium confined in pores. One of the thermometers is a superconductive transition thermometer (STT). The STT has a temperature resolution of about 5nK. The other high resolution thermometer described is a magnetic susceptibility thermometer. This thermometer measures the magnetization of copper ammonium bromide (CAB) using a SQUID magnetometer. The CAB thermometer has an observed sensitivity of about 20nK. Suggestions for improvements in both thermometers are made. Simulation work on the temperature profile of a thermal conductivity cell near Tlambda is described. The simulations are compared with the experimental results, and a careful study of the stability of the numerics is described. The study of helium confined into pores and films is described next. Both previous theoretical and experimental work on finite size effects in liquid helium are described. The geometry provided by glass capillary arrays is analyzed to determine what would be observed when the specific heat of helium confined to the arrays is measured. Finally, I describe my measurements of the isobaric thermal expansion coefficient beta_ {rm p} of 4He confined in an aerogel for several isobars along the lambda -line. beta_{rm p} is an asymptotically linear function of C _{rm p} near the superfluid transition temperature T_{rm c}. Therefore, fits to power laws in t equiv T/T_{c} - 1 give the specific heat exponents alpha and alpha^' and amplitude ratio A^'/A. Such fits gave different exponents alpha ~ -0.6 and alpha^ ' ~ -1.0 above and below T _{c}. When an analytic background term a times t was included in the fit, a pressure-independent value of alpha = alpha^' ~ -0.59 was permitted, but A^' /A was found to be near zero. Measurements of rho_{rm s}/ rho when fit to a power law gave a pressure-independent value zeta = 0.755 +/- 0.003. Through hyperscaling this implies alpha^' = -0.25 which can not be reconciled with our beta_{rm p} measurements. The current theoretical understanding of the problem of helium in aerogel is also discussed.