Question

Consider a thermal engine filled with N molecules of a monatomic ideal gas. The gas undergoes a cyclic transformation, as shown. (Figure 1)Processes AB and CD are isothermal (constant temperature), and processes BC and DA are isochoric (constant volume). The quantities P1, P2, V1, and V2 are defined in the figure. For example, when the gas is in state A, it has pressure P2 and volume V1; when the gas is in state B, it has volume V2, but the pressure is not given.

Answer 1

An isothermal process is one in which the temperature of the system remains constant throughout the process. Processes AB and CD in the given thermal engine are isothermal, while processes BC and DA are isochoric. Understanding these processes allows for the calculation of work done, heat exchanged, and changes in internal energy.

Step-by-step explanation:

An isothermal process is one in which the temperature of the system remains constant throughout the process. In the given scenario, processes AB and CD are isothermal, meaning that the temperature of the gas remains constant during these processes. On the other hand, processes BC and DA are isochoric, which means the volume of the gas remains constant.

During an isothermal process, the pressure and volume of the gas are inversely proportional, according to the ideal gas law equation PV = nRT. Since the temperature is constant, the equation simplifies to P1V1 = P2V2.

By understanding the nature of the isothermal and isochoric processes in this thermal engine, one can analyze the various states of the gas and calculate quantities such as work done, heat exchanged, and changes in internal energy.

Answer 2

The student's question involves examining thermodynamic processes, specifically isothermal and isochoric, in a cycle involving a monatomic ideal gas and requires understanding of the concepts such as temperature, volume, and pressure.

Step-by-step explanation:

The question relates to a monatomic ideal gas undergoing a series of thermodynamic processes in a cyclic transformation. Initially, the gas is expanded isothermally, meaning the temperature remains constant, and then it is cooled isochorically, which implies the volume remains unchanged while the pressure decreases.

In continuation, the gas is compressed back isothermally to its original volume but with reduced pressure, and it is finally heated isochorically to return to its initial state. Throughout these transitions, the characteristics of isothermal and isochoric processes are crucial. For isothermal processes, the correlation PV = nRT is constant, since the number of moles n, the gas constant R, and temperature T are unchanged. During isochoric processes, no work is done since volume is constant, meaning any heat added changes the internal energy directly.