A vertical cylinder of cross sectional area A is fitted with a tight-fitting, frictionless piston of mass m (figure below). Gas (a) If n moles of an ideal gas are in the cylinder at a temperature of T, use Newton's second law for equilibrium to show that the height h at which the piston is in equilibrium under its own weight is given by nRT h = mg + PA where P, is atmospheric pressure. (Submit a file with a maximum size of 1 MB.) Choose FileNo file chosen This answer has not been graded yet. (b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure? O less than O equal to O greater than

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Chapter1: Units, Trigonometry. And Vectors
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**Vertical Cylinder with Piston**

A vertical cylinder with a cross-sectional area \( A \) is fitted with a tight-fitting, frictionless piston of mass \( m \).

**Diagram Explanation:**
- The illustration shows a vertical cylinder containing gas.
- A piston, labeled with mass \( m \), is positioned above the gas.
- The height of the gas column is indicated as \( h \).
- The cross-sectional area of the cylinder is denoted by \( A \).

**Questions:**

(a) If \( n \) moles of an ideal gas are in the cylinder at a temperature \( T \), use Newton's second law for equilibrium to show that the height \( h \) at which the piston is in equilibrium under its own weight is given by

\[
h = \frac{nRT}{mg + P_0 A}
\]

where \( P_0 \) is atmospheric pressure.

*Submit a file (maximum size: 1 MB).*

*Note: This answer has not been graded yet.*

(b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure?

- ○ less than
- ○ equal to
- ○ greater than
Transcribed Image Text:**Vertical Cylinder with Piston** A vertical cylinder with a cross-sectional area \( A \) is fitted with a tight-fitting, frictionless piston of mass \( m \). **Diagram Explanation:** - The illustration shows a vertical cylinder containing gas. - A piston, labeled with mass \( m \), is positioned above the gas. - The height of the gas column is indicated as \( h \). - The cross-sectional area of the cylinder is denoted by \( A \). **Questions:** (a) If \( n \) moles of an ideal gas are in the cylinder at a temperature \( T \), use Newton's second law for equilibrium to show that the height \( h \) at which the piston is in equilibrium under its own weight is given by \[ h = \frac{nRT}{mg + P_0 A} \] where \( P_0 \) is atmospheric pressure. *Submit a file (maximum size: 1 MB).* *Note: This answer has not been graded yet.* (b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure? - ○ less than - ○ equal to - ○ greater than
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