The thermodynamics of interplanetary coronal mass ejections (ICMEs) is often described using a polytropic process. Estimating the polytopic index ( \(\gamma \) ) allows us to quantify the expansion or compression of the ICME plasma arising from changes in the plasma temperature. In this study, we estimate \(\gamma \) for protons inside the magnetic clouds (MCs), their associated sheaths, and ambient solar wind for a large sample of well-observed events observed by the Wind spacecraft at 1 AU. We find that \(\gamma \) shows a high ( \({\approx }1.6\) ) – low ( \({\approx } 1.05\) ) – high ( \({\approx }1.2\) ) behavior inside the ambient solar wind, sheath, and MCs, respectively. We also find that the proton polytropic index is independent of small-scale density fluctuations. Furthermore, our results show that the stored energy inside MC plasma is not expended in expanding its cross-section at 1 AU. The sub-adiabatic nature of MC plasma implies external heating – possibly due to thermal conduction from the corona. We find that the heating gradient per unit mass from the corona to the protons of MC at 1 AU is \({\approx } 0.21\) erg cm \(^{-1}\) g \(^{-1}\) , which is in agreement with the required proton heating budget.
