The　irreversible　losses　including　intake　pressure,　leakage,　heat　transfer,　friction　and　over-expansion　losses　have　great　influence　on　the　expander　performance.　In　this　paper,　a　thermodynamic　model　is　presented　to　predict　the　real　expansion　process　exponent　and　analyze　the　under-expansion　or　over-expansion　under　designed　and　off-designed　operation　conditions.　The　model　verified　by　experimental　results　has　a　good　agreement.　Results　showed　that　the　real　expansion　process　exponent　of　air　is　higher　than　the　ideal　adiabatic　index　of　1.4　and　decreases　from　1.716　to　1.644　with　the　internal　volume　ratio　changing　from　1.8　to　6.5.　The　real　expansion　process　exponent　of　R123　is　close　to　1.00　under　different　internal　volume　ratio.　Compared　to　the　intake　pressure,　the　variation　of　back　pressure　has　greater　influence　on　the　large　internal　volume　ratio　than　the　small　one.　Thus,　to　adjust　the　back　pressure　is　more　effective　to　match　the　designed　condition　for　the　expander　with　a　large　internal　volume　ratio.