ɪnðɪ ˈɜːli nˈaɪntiːnθ sˈɛntʃɚɹi θˌɜːmoʊdaɪnˈæmɪsˌɪsts sˈʌtʃ ɐz sˈædi kˈɑːɹnɑːt, ɹˈuːdɑːlf klˈɔːsɪəs, ænd ɪmˈaɪl klˈeɪpɪɹən dɪvˈɛləpt mˌæθɪmˈæɾɪkəl mˈɑːdəlz ɔnðə daɪnˈæmɪks ʌv flˈuːɪd bˈɑːdiz ænd vˈeɪpɚz ɹᵻlˈeɪɾᵻd tə ðə kəmbˈʌstʃən ænd pɹˈɛʃɚ sˈaɪkəlz ʌv ˌætməsfˈɛɹɪk stˈiːm ˈɛndʒɪnz; wˈʌn ɛɡzˈæmpəl ɪz ðə klˈɔːsɪəs klˈeɪpɪɹən ᵻkwˈeɪʒən.
In the early 19th century thermodynamicists such as Sadi Carnot, Rudolf Clausius, and Émile Clapeyron developed mathematical models on the dynamics of fluid bodies and vapors related to the combustion and pressure cycles of atmospheric steam engines; one example is the Clausius–Clapeyron equation.