Q. 61

Expert-verifiedFound in: Page 546

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Two cylinders each contain of a diatomic gas at and a pressure of . Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is .

a. What are the final temperature and volume of each?

b. Show both processes on a single diagram. Use an appropriate scale on both axes.

a. The final temperature and volume of each cylinder is and respectively.

b. Thediagram is as follows:

Amount of diatomic gas in two cylinders

Temperature

Pressure

Cylinder A expands isothermally till the pressure reach

Cylinder B expands adiabatically till the pressure reach

(a) Since cylinder A expands isothermally, by definition, its temperature after the expansion will be the same as before; that is .

Knowing that the expansion was isothermic, we have

The initial volume can be found from the Ideal Gas Law:

Therefore, the final volume of cylinder A will be

For cylinder B we have an adiabatic process, which means that

We need to find an expression for .

We have,

Finally,

For diatomic gases we have , and we know that the pressure ratio is , as well as the fact that the initial volume was Liters.

We therefore can calculate numerically,

As for the temperature, from the Ideal Gas Law, we can find that,

Amount of diatomic gas in two cylinders

Temperature

Pressure

Cylinder A expands isothermally till the pressure reach

Cylinder B expands adiabatically till the pressure reach

An approximate graphical representation of the situation is given below:

Therefore, the diagram is as follows:

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