A new air-flow modelling approach for respiratory-chamber indirect calorimetry is introduced. Based on thermodynamic theory, differential equations describing the dynamics of the calorimeter are derived. These equations are then developed into a linear state space model that can be conceptualized as a modern control system. Furthermore, both the system/output noises and input/output delays are considered in the model in the context of real applications. Finally, system accuracy is analysed so that the parameters in the calorimeter can be selected to minimise the error in estimating energy expenditure in humans.