What is the net work output per cycle for the thermodynamic...

What is the net work output per cycle for the thermodynamic cycle in Fig. $20-4$ ? We know that the net work output per cycle is the area enclosed by the $P-V$ diagram. We estimate that in area $A B C A$ there are 22 squares, each of area $$\left(0.5 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\right)\left(0.1 \mathrm{~m}^{3}\right)=5 \mathrm{~kJ}$$ Therefore, Area enclosed by cycle $\approx(22)(5 \mathrm{~kJ})=1 \times 10^{2} \mathrm{~kJ}$ The net work output per cycle is $1 \times 10^{2} \mathrm{~kJ}$.

What is the net work output per cycle for the thermodynamic cycle in Fig. $20-4$ ?
We know that the net work output per cycle is the area enclosed by the $P-V$ diagram. We estimate that in area $A B C A$ there are 22 squares, each of area
$$\left(0.5 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\right)\left(0.1 \mathrm{~m}^{3}\right)=5 \mathrm{~kJ}$$
Therefore,
Area enclosed by cycle $\approx(22)(5 \mathrm{~kJ})=1 \times 10^{2} \mathrm{~kJ}$
The net work output per cycle is $1 \times 10^{2} \mathrm{~kJ}$.

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Key Concepts

Pressure-Volume (P-V) Diagram

A P-V diagram graphically represents the changes in pressure and volume of a system during a thermodynamic process. The area enclosed by a cycle on this diagram is directly proportional to the net work output, making it an essential tool for visualizing and calculating the work done in a cyclic process.

Net Work Output

The net work output in a thermodynamic cycle is defined as the total work done by the system during one complete cycle. It is equal to the area enclosed by the process path on a pressure-volume (P-V) diagram, representing the energy transferred as work during the cycle.

Area Estimation Method

The calculation of net work output can involve estimating the area enclosed by a cycle on a P-V diagram. This is often achieved by dividing the area into smaller, manageable sections, such as squares, whose areas are computed based on the provided scales for pressure and volume, and then summing these areas to approximate the total work output.

Dimensional Analysis

Ensuring that the units are consistent is critical when calculating work output. In thermodynamics, pressure multiplied by volume yields energy (work) with units such as joules or kilojoules. Correct dimensional analysis guarantees the validity of the calculation and the physical meaning of the result.

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