Mastering Adiabats

just shown the adiabats for one mole of an ideal gas:

Conclusion

In this lecture, we have explored the behavior of ideal gases in the pressure and temperature range corresponding to heat engines. We have learned how gases absorb heat and turn it into work, and vice versa, and how the interplay of heat and work is called thermodynamics. We have also discussed the specific heats of gases at constant volume and constant pressure, and how they relate to the internal energy of the gas and the work it does. Finally, we have seen how the behavior of gases can be tracked in the (P, V) plane using isotherms and adiabats, and how these curves relate to the transfer of heat and work in a heat engine.The text describes the equation for an adiabat and how it corresponds to an isotherm. It explains that the change in internal energy when the gas temperature is raised is equal to the product of the heat capacity at a constant volume and the change in temperature. In adiabatic compression, all the work done by the external pressure goes into the internal energy. The equation of an adiabat can be found by integrating the equation for an isotherm, resulting in the equation T/V^(γ-1) = constant, where γ is the ratio of the heat capacities. For a monatomic gas, γ is 5/3, and for a diatomic gas, γ is 7/5. The equation for an adiabat in terms of P and V is P*V^γ = constant.