The atmosphere is an example of a non-equilibrium system. This study explores the relationship among temperature, energy and entropy of the atmosphere, introducing two variables that serve to quantify the thermodynamic disequilibrium of the atmosphere. The maximum work, Wmax, that the atmosphere can perform is defined as the work developed through a thermally reversible and adiabatic approach to thermodynamic equilibrium with global entropy conserved. The maximum entropy increase, (ΔS)max, is defined as the increase in global entropy achieved through a thermally irreversible transition to thermodynamic equilibrium without performing work. Wmax is identified as an approximately linear function of (ΔS)max. Large values of Wmax or (ΔS)max correspond to states of high thermodynamic disequilibrium. The seasonality and long-term historical variation of Wmax and (ΔS)max are computed, indicating highest disequilibrium in July, lowest disequilibrium in January with no statistically significant trend over the past 32 years. The analysis provides a perspective on the interconnections of temperature, energy and entropy for the atmosphere and allows for a quantitative investigation of the deviation of the atmosphere from thermodynamic equilibrium.