The Restricted Access Window (RAW) mechanism introduced in the IEEE 802.11ah standard aims to address the high channel contention of Internet of Things (IoT) networks. It allows the Access Point (AP) to periodically limit channel access to only one group of stations during a short time interval called RAW slot. Such a time limit prevents the channel access contention from reaching the steady state. Henceforth, we present a renewal theory based analytical model for the time-limited contention within the RAW slot. Furthermore, we construct a counting process to track transmissions within the contention interval and derive closed-form analytical results. As IoT networks are typically composed of battery-powered devices, it is compulsory to manage the energy consumption of the network in order to extend the lifetime of devices. Hence, we analyze and evaluate the energy consumption and energy efficiency during the RAW slot period. Extensive simulations using Matlab software validate the analytical model and prove the effectiveness of our proposals.