Ammonia vapor is compressed inside a cylinder by an external...

Ammonia vapor is compressed inside a cylinder by an external force acting on the piston. The ammonia is initially at $30^{\circ} \mathrm{C}, 500 \mathrm{kPa}$, and the final pressure is $1400 \mathrm{kPa}$. The following data have been measured for the process: $$\begin{array}{clllllll} \hline \text { Pressure, } & 500 & 653 & 802 & 945 & 1100 & 1248 & 1400 \\ \mathrm{kPa} & & & & & & \\ \text { Volume, L } & 1.25 & 1.08 & 0.96 & 0.84 & 0.72 & 0.60 & 0.50 \\ \hline \end{array}$$ Determine the work done by the ammonia by summing the area below the $P-V$ process curve. As you plot it, $P$ is the height and the change in volume is the base of a number of rectangles.

Ammonia vapor is compressed inside a cylinder by an external force acting on the piston. The ammonia is initially at $30^{\circ} \mathrm{C}, 500 \mathrm{kPa}$, and the final pressure is $1400 \mathrm{kPa}$. The following data have been measured for the process: $$\begin{array}{clllllll}
\hline \text { Pressure, } & 500 & 653 & 802 & 945 & 1100 & 1248 & 1400 \\
\mathrm{kPa} & & & & & & \\
\text { Volume, L } & 1.25 & 1.08 & 0.96 & 0.84 & 0.72 & 0.60 & 0.50 \\
\hline
\end{array}$$ Determine the work done by the ammonia by summing the area below the $P-V$ process curve. As you plot it, $P$ is the height and the change in volume is the base of a number of rectangles.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Pressure-Volume (P-V) Diagram

A P-V diagram is used in thermodynamics to graphically represent the relationship between the pressure and volume of a system during a process. The plot helps visualize how the state of the system changes, and importantly, the area under the process curve can be interpreted as the work done by or on the system.

Thermodynamic Work

In thermodynamics, work is defined as the energy transferred when a force moves the boundary of a system. For a process occurring in a piston-cylinder assembly, the work done is calculated as the integral of pressure with respect to volume. This integral corresponds to the area under the P-V curve, providing a means to quantify the work during expansion or compression.

Numerical Integration

When data for pressure and volume are available at discrete intervals rather than as a continuous function, numerical integration techniques such as the rectangular method or trapezoidal rule are employed. These methods approximate the area under the P-V curve by summing the contributions of small segments, allowing for an estimation of the work done in the process.

Transcript

Please give Ace some feedback