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Q. 51

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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

51. A concrete table needs to be supported at the four corners by compressed-air cylinders. Each cylinder is in diameter and has a initial length when the pressure inside is . A hoist lowers the table very slowly, compressing the cylinders while allowing them to stay in thermal equilibrium with their surroundings. How much work has been done on the gas of the four cylinders when the table reaches its equilibrium position?

The amount of work has been done on the gas of the four cylinders when the table reaches its equilibrium position is,

See the step by step solution

Step by Step Solution

Step 1: Given Information

Concrete table weight

Diameter of the cylinder

Initial length

Pressure

Step 2: Explanation 

It is clear from the text that this is an isothermal process.

The work in an isothermal process is given by,

What we need to find is the volume ratio, the number of moles, and the temperature Since this is an isothermal process, we can write that

As for the pressures, on the other side, we know that while the second pressure will be,

Step 3: Explanation 

The added term is the pressure coming from the weight distributed on the four cylinders with total cross-section area . Knowing the diameter of all these cylinders and the fact that there are 4 such cylinders, we can write that

This means that we now know the volume ratio to be

As for , let's express this by the Ideal Gas Law: we'll see that this will solve us our problem.

Substituting in the expression for the work, we have

Substituting, and taking note that we just need to put values of the pressure and volume at the beginning from the same instant -- let this be the initial values, we have

Step 4: Final Answer

Substituting our numerical values, we have

Multiply the expression,

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