We propose a process calculus for modelling and reasoning on systems in the Internet of Things paradigm. Our systems interact both with the physical environment, via sensors and actuators, and with smart devices, via short-range and Internet channels. The calculus is equipped with a standard notion of labelled bisimilarity which represents a fully abstract characterisation of a well-known contextual equivalence. We use our semantic proof-methods to prove run-time properties of a non-trivial case study as well as system equalities.