A cylinder that has a 41.5-cm radius and is 50.0 cm deep is filled with air at 29.0°C and 1.00 atm shown in figure (a). A 24.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi as shown in figure (b). Finally, a 27.0-kg dog stands on the piston, further compressing the air, which remains at 29.0°C as shown in figure (c). (a) How far down (Δh) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and the dog back to hi?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A cylinder that has a 41.5-cm radius and is 50.0 cm deep is filled with air at 29.0°C and 1.00 atm shown in figure (a). A 24.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi as shown in figure (b). Finally, a 27.0-kg dog stands on the piston, further compressing the air, which remains at 29.0°C as shown in figure (c).

(a) How far down (Δh) does the piston move when the dog steps onto it?

(b) To what temperature should the gas be warmed to raise the piston and the dog back to hi?

The image consists of three diagrams labeled (a), (b), and (c), which illustrate the changes in fluid height within a container:

- **Diagram (a):** A U-shaped container is shown, fully empty, with a height marked as 50.0 cm. This indicates the total internal height of the container.

- **Diagram (b):** The same container is now partially filled with a liquid. The liquid level is marked as \( h_i \), representing the initial height of the fluid within the container.

- **Diagram (c):** An object in the shape of a dog is placed above the liquid, causing the fluid level to rise. The change in height from the initial liquid level \( h_i \) is indicated as \( \Delta h \). This demonstrates how the volume of the object affects the fluid height due to displacement.

This sequence is often used to teach principles related to fluid displacement and Archimedes' principle.
Transcribed Image Text:The image consists of three diagrams labeled (a), (b), and (c), which illustrate the changes in fluid height within a container: - **Diagram (a):** A U-shaped container is shown, fully empty, with a height marked as 50.0 cm. This indicates the total internal height of the container. - **Diagram (b):** The same container is now partially filled with a liquid. The liquid level is marked as \( h_i \), representing the initial height of the fluid within the container. - **Diagram (c):** An object in the shape of a dog is placed above the liquid, causing the fluid level to rise. The change in height from the initial liquid level \( h_i \) is indicated as \( \Delta h \). This demonstrates how the volume of the object affects the fluid height due to displacement. This sequence is often used to teach principles related to fluid displacement and Archimedes' principle.
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