An ideal gas within a piston-cylinder assembly executes a...

An ideal gas within a piston-cylinder assembly executes a Carnot power cycle. as shown in Fig. 5.13. The isothermal compression occurs at $300 \mathrm{~K}$ from $90 \mathrm{kPa}$ to $120 \mathrm{kPa}$. If the thermal efficiency is $60 \%$, determine (a) the temperature of the isothermal expansion, in $K$, and (b) the net work developed, in kJ per kmol of gas.

Key Concepts

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle composed of two isothermal processes and two adiabatic processes. It represents the maximum possible efficiency that any heat engine operating between two thermal reservoirs can achieve. In a Carnot power cycle, the working substance undergoes reversible processes, making it a benchmark for comparing real engine performances.

Carnot Efficiency

Carnot efficiency is defined as the theoretical efficiency of a Carnot engine and is expressed as 1 - (T_low/T_high), where T_low and T_high are the absolute temperatures of the cold and hot reservoirs respectively. This relation underlines how the efficiency of an engine improves when the temperature difference between the heat source and sink increases.

Isothermal Process

An isothermal process is one in which the temperature of the working substance remains constant. In the context of an ideal gas, this implies that any heat transfer into or out of the system is entirely used to perform work, since the internal energy does not change. Both the expansion and compression stages in the Carnot cycle are isothermal processes.

Net Work Calculation

Net work calculation in a thermodynamic cycle involves finding the difference between the work done by the system during the expansion phase and the work done on the system during the compression phase. For reversible cycles like the Carnot cycle, net work is directly related to the heat input and the cycle's efficiency.

Ideal Gas Behavior

Ideal gas behavior assumes that the gas molecules do not interact except through elastic collisions and that the volume of the molecules is negligible compared to the volume of the container. This assumption simplifies the analysis of thermodynamic processes, such as those in a Carnot cycle, by allowing the application of the ideal gas law to relate pressure, volume, and temperature during different parts of the cycle.

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