A Carnot cycle is executed in a closed system and uses 0.0025 kg of air as the working fluid. T

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A Carnot cycle is executed in a closed system and uses...

A Carnot cycle is executed in a closed system and uses $0.0025 \mathrm{~kg}$ of air as the working fluid. The cycle efficiency is 60 percent, and the lowest temperature in the cycle is $300 \mathrm{~K}$. The pressure at the beginning of the isentropic expansion is $700 \mathrm{kPa}$, and at the end of the isentropic compression it is $1 \mathrm{MPa}$. Determine the net work output per cycle.

Key Concepts

Net Work Output

Net work output is calculated as the difference between the heat absorbed during the heating phase and the heat rejected during the cooling phase of the cycle. In the Carnot cycle, the net work is directly linked to the thermal efficiency and the magnitude of the heat input, providing a measure of the useful energy produced per cycle in a closed system.

Closed System

A closed system in thermodynamics is one in which the mass remains constant over time while energy in the form of heat and work may be exchanged with the surroundings. In cycle analyses like the Carnot cycle, assuming a closed system allows for precise tracking of energy transformations and simplifies the calculation of work and heat transfer.

Heat Transfer in Isothermal Processes

During the isothermal processes of the Carnot cycle, the working fluid either absorbs or rejects heat at a constant temperature. This controlled heat transfer is crucial for maintaining the reversibility of the process and directly affects the work output and efficiency of the cycle.

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that defines the maximum possible efficiency any heat engine operating between two heat reservoirs can achieve. It consists of two isothermal processes (heat transfer at constant temperature) and two adiabatic (isentropic) processes (no heat transfer with constant entropy), forming a reversible cycle used as a benchmark in thermodynamic analyses.

Thermal Efficiency

Thermal efficiency in thermodynamics is the ratio of the net work output of an engine to the heat input. For a Carnot engine, this efficiency is uniquely determined by the temperatures of the hot and cold reservoirs, emphasizing that higher efficiency is achieved by increasing the temperature difference between the reservoirs.

Isentropic Process

An isentropic process is one in which the entropy of the system remains constant, implying that the process is both adiabatic (no heat exchange) and reversible. In the context of the Carnot cycle, the isentropic expansion and compression steps are essential for transferring the system between the two isothermal states without energy losses due to irreversibilities.

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