In this paper we study thermodynamic properties of hydrogen and hydrogen-helium mixtures with the help of the direct path integral Monte Carlo simulations. The results are compared with available theoretical and experimental methods based, in particular, on chemical picture. We investigate the effects of temperature ionization in low-density hydrogen plasma. We also present a number of calculated isotherms for hydrogenhelium mixture with the mass concentration of helium Y = 0.234 in the range from 10 4 K to 2 · 10 5 K. In the density region where a sharp conductivity rise have been observed experimentally the simulations give indications for one or two plasma phase transitions, in accordance with earlier theoretical predictions.