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Q. 32

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 567

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Short Answer

A cylinder of nitrogen gas has a volume of and a pressure of atm.
a. What is the thermal energy of this gas at room temperature ?b. What is the mean free path in the gas?c. The valve is opened and the gas is allowed to expand slowly and isothermally until it reaches a pressure of atm . What is the change in the thermal energy of the gas?

a)The Thermal energy of gas is
b)The Mean free path in tha gas isc)The change in thermal energy of the gas is Zero.

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Step by Step Solution

Step: 1   Finding the Thermal Energy of gas at  room temperature: (part a)

Because nitrogen is a diatomic gas, the thermal energy is calculated as follows:

Now we know that ,

From equation andwe get that

Given that and , then substituting these to the formula:

Step: 2  Finding the Mean free path: (part b)

The mean free path is given by

Now we have

and for nitrogen is ,then the mean free path will be:

Step: 3  Change in Thermal Energy of gas: (part c)

But even though the formula shows that thermal energy is proportional to the number of gas molecules, degrees of freedom, and gas temperature, none of these factors change in this isothermal expansion.

As a result, the total amount of thermal energy will remain unchanged. Thermal energy will remain unchanged.

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