1. A gas fills the right portion of a horizontal cylinder whose radius is 5.30 cm. The initial pressure of the gas is 1.01 x10° Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. N/m Unstrained spring Pin
1. A gas fills the right portion of a horizontal cylinder whose radius is 5.30 cm. The initial pressure of the gas is 1.01 x10° Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. N/m Unstrained spring Pin
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![1. A gas fills the right portion of a horizontal cylinder whose radius is 5.30 cm. The initial pressure of the gas is \(1.01 \times 10^5 \, \text{Pa}\). A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.
[Blank for answer] N/m
---
**Explanation of Diagram:**
The diagram shows a horizontal cylinder. Inside the cylinder:
- On the left side, there is an unstrained spring.
- The spring is in contact with a movable piston.
- The piston separates the spring from the gas on the right side.
- A pin holds the piston in place initially.
- The right side of the cylinder is filled with gas.
The scenario demonstrates the mechanical and thermodynamic principles involving gas expansion and spring mechanics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c9fffcb-a146-4185-bf71-b31903a19d20%2F9682fe46-9080-4bf9-88e7-971cd6720bd6%2Fg394gt9_processed.png&w=3840&q=75)
Transcribed Image Text:1. A gas fills the right portion of a horizontal cylinder whose radius is 5.30 cm. The initial pressure of the gas is \(1.01 \times 10^5 \, \text{Pa}\). A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.
[Blank for answer] N/m
---
**Explanation of Diagram:**
The diagram shows a horizontal cylinder. Inside the cylinder:
- On the left side, there is an unstrained spring.
- The spring is in contact with a movable piston.
- The piston separates the spring from the gas on the right side.
- A pin holds the piston in place initially.
- The right side of the cylinder is filled with gas.
The scenario demonstrates the mechanical and thermodynamic principles involving gas expansion and spring mechanics.
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