Context. G29.96-0.02 is a high-mass star-forming cloud observed at 70, 160, 250, 350, and 500 {$μ$}m as part of the Herschel survey of the Galactic plane (Hi-GAL) during the science demonstration... Show moreContext. G29.96-0.02 is a high-mass star-forming cloud observed at 70, 160, 250, 350, and 500 {$μ$}m as part of the Herschel survey of the Galactic plane (Hi-GAL) during the science demonstration phase. Aims: We wish to conduct a far-infrared study of the sources associated with this star-forming region by estimating their physical properties and evolutionary stage, and investigating the clump mass function, the star formation efficiency and rate in the cloud. Methods: We have identified the Hi-GAL sources associated with the cloud, searched for possible counterparts at centimeter and infrared wavelengths, fitted their spectral energy distribution and estimated their physical parameters. Results: A total of 198 sources have been detected in all 5 Hi-GAL bands, 117 of which are associated with 24 {$μ$}m emission and 87 of which are not associated with 24 {$μ$}m emission. We called the former sources 24 {$μ$}m-bright and the latter ones 24 {$μ$}m-dark. The [70-160] color of the 24 {$μ$}m-dark sources is smaller than that of the 24 {$μ$}m-bright ones. The 24 {$μ$}m-dark sources have lower L$_{bol}$ and L$_{bol}$/M$_{env}$ than the 24 {$μ$}m-bright ones for similar M$_{env}$, which suggests that they are in an earlier evolutionary phase. The G29-SFR cloud is associated with 10 NVSS sources and with extended centimeter continuum emission well correlated with the 70 {$μ$}m emission. Most of the NVSS sources appear to be early B or late O-type stars. The most massive and luminous Hi-GAL sources in the cloud are located close to the G29-UC region, which suggests that there is a privileged area for massive star formation toward the center of the G29-SFR cloud. Almost all the Hi-GAL sources have masses well above the Jeans mass but only 5% have masses above the virial mass, which indicates that most of the sources are stable against gravitational collapse. The sources with M$_{env}$ {gt} M$_{virial}$ and that should be undergoing collapse and forming stars are preferentially located at {lsim}4' of the G29-UC region, which is the most luminous source in the cloud. The overall SFE of the G29-SFR cloud ranges from 0.7 to 5%, and the SFR ranges from 0.001 to 0.008 M$_{⊙}$ yr$^{-1}$, consistent with the values estimated for Galactic Hii regions. The mass spectrum of the sources with masses above 300 M$_{⊙}$, well above the completeness limit, can be well-fitted with a power law of slope {$α$} = 2.15 {plusmn} 0.30, consistent with the values obtained for the whole l = 30{deg}, associated with high-mass star formation, and l = 59{deg}, associated with low- to intermediate-mass star formation, Hi-GAL SDP fields. Tables 1-3 are available in electronic form at http://www.aanda.orgShow less
