  The magnetic susceptibility chi and specific heat C versus temperature T of
the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg
chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation
parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed
comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper
and Johnston are made with the asymptotically exact low-T field theory
predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T)
are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is
extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above
numerical data are obtained. We examine in detail the theoretical predictions
of Bulaevskii for chi(alpha,T) and compare them with our results. Our
experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in
detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are
not in agreement with the prediction for the uniform Heisenberg chain, but can
be explained if there is a moderate ferromagnetic interchain coupling and/or if
J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2)
K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and
average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are
derived from the data. A spin pseudogap with a large magnitude \approx 0.4
Delta(0) is consistently found just above Tc, which decreases with increasing
T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy
change due to the transition at Tc and associated order parameter fluctuations
arise from the lattice and/or charge degrees of freedom and less than 23% from
the spin degrees of freedom.
