Abstract We assume the non-flat Friedmann-Robertson-Walker (FRW) Universe as a thermodynamical system. We assume the cosmological horizon as an inner trapping horizon which is treated as dynamical apparent horizon of FRW Universe. We write the dynamical apparent horizon radius and temperature on the apparent horizon. We assume that the fluid pressure as thermodynamical pressure of the system. Using Hayward's unified first law, Clausius relation and Friedmann equations with cosmological constant, we obtain the entropy on the apparent horizon. We assume that the cosmological constant provides the thermodynamic pressure of the system. We obtain the entropy, surface area, volume, temperature, Gibb's Helmholtz's free energies, specific heat capacity of the FRW Universe due to the thermodynamic system. We study the Joule-Thomson expansion of the FRW Universe and by evaluating the positive sign of Joule-Thomson coefficient, we determine that the FRW Universe obeys the cooling nature. We also find the inversion temperature and inversion pressure. Next we demonstrate the thermodynamical FRW Universe as heat engine. For Carnot cycle, we obtain the work done and the maximum efficiency. Also for new engine, we study the work done and its efficiency.

中文翻译：

---

FRW 宇宙的热力学：热机

摘要 我们假设非平坦的弗里德曼-罗伯逊-沃克 (FRW) 宇宙是一个热力学系统。我们假设宇宙视界是一个内陷视界，它被视为 FRW 宇宙的动态视界。我们在视地平线上写下动态视地平线半径和温度。我们假设流体压力为系统的热力学压力。使用海沃德统一第一定律、克劳修斯关系和具有宇宙常数的弗里德曼方程，我们得到视视界的熵。我们假设宇宙常数提供了系统的热力学压力。由于热力学系统，我们获得了 FRW 宇宙的熵、表面积、体积、温度、吉布斯亥姆霍兹自由能、比热容。我们研究了FRW宇宙的Joule-Thomson膨胀，通过评估Joule-Thomson系数的正号，我们确定FRW宇宙服从冷却性质。我们还找到了反转温度和反转压力。接下来，我们将热力学 FRW 宇宙演示为热机。对于卡诺循环，我们得到完成的功和最大的效率。同样对于新引擎，我们研究所做的工作及其效率。