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Q. 55

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 545

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Short Answer

55. An diameter, well-insulated vertical cylinder containing nitrogen gas is sealed at the top by a frictionless piston. The air pressure above the piston is

a. What is the gas pressure inside the cylinder?

b. Initially, the piston height above the bottom of the cylinder is . What will be the piston height if an additional are placed on top of the piston?

a. The gas pressure inside the cylinder is

b. The piston height if an additional are placed on top of the piston is

See the step by step solution

Step by Step Solution

Step 1: Given Information (Part a)

Diameter of the well-insulated vertical cylinder

Cylinder Sealed at the top frictionless piston

Pressure

Step 2: Explanation (Part a)

(a) The pressure of the gas, will be equal to the external pressure and the pressure coming from the weight of the mass . This pressure is therefore

Numerically, we have

Step 3: Final Answer (Part a)

Hence, gas pressure inside the cylinder is .

Step 4: Given Information (Part b)

Diameter of the well-insulated vertical cylinder

Cylinder Sealed at the top frictionless piston

Pressure

The piston height above the bottom of the cylinder is

Additional height

Step 5: Explanation (Part b)

(b) This will be an isothermal process. We therefore know that

Since the volume is a cylinder with basis , we have

We thus need to find the pressure after the second mass is added.

Analogously to the first example, we have

Substitute the values,

Step 6: Final Answer (Part b)

Substituting, we find the height after the second mass is added to be

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