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Energy consumption is of utmost importance in wireless mesh networks where nodes are battery operated and have limited power resources. In this paper, we develop an analytical model to estimate the throughput-capacity of a wireless mesh network and use this model to study the network's bit-per-joule performance. We assume that each node uses an IEEE 802.11 based software controlled radio whose modulation/coding scheme and rate can be dynamically selected. A topology synthesis algorithm is used to elect nodes to act as access points as well as backbone nodes (BNs). The latter form a mesh backbone network infrastructure. We present an algorithm that is used to analytically calculate an approximation of the throughput capacity performance of the network. We use this algorithm to examine the performance efficiency of the network, expressed in terms of the throughput rate per unit energy consumed under the joint setting of nodal transmit power and data rate levels. Our results show that when traffic is uniformly distributed across the area of operations, increasing the nodal transmit power levels, as well as the data rates, tend often to enhance the bit-per-joule performance of the system. We also examine the impact of the selection of the transmit data rate and power levels used in conducting the topology synthesis of the backbone network.