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Q. 61

Expert-verified
Found in: Page 546

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

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:

See the step by step solution

Step 1: Given Information (Part a)

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

Step 2: Explanation (Part a)

(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,

Step 3: Final Answer (Part a)

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

Step 4: Given Information (Part b)

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

Step 5: Explanation (Part b)

An approximate graphical representation of the situation is given below: