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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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Gas law calculations Consider the Ideal Gas Law PV = kT,

Chapter 12, Problem 41E

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QUESTION:

Gas law calculations  Consider the Ideal Gas Law PV=kT, where k>0 is a constant. Solve this equation for V in terms of P and T.

(a) Determine the rate of change of the volume with respect to the pressure at constant temperature. Interpret the result.

(b) Determine the rate of change of the volume with respect to the temperature at constant pressure. Interpret the result.

(c) Assuming k=1, draw several level curves of the volume function and interpret the results as in Example 5.

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QUESTION:

Gas law calculations  Consider the Ideal Gas Law PV=kT, where k>0 is a constant. Solve this equation for V in terms of P and T.

(a) Determine the rate of change of the volume with respect to the pressure at constant temperature. Interpret the result.

(b) Determine the rate of change of the volume with respect to the temperature at constant pressure. Interpret the result.

(c) Assuming k=1, draw several level curves of the volume function and interpret the results as in Example 5.

ANSWER:

Solution 41E

Given

Consider the Ideal Gas Law PV = kT, where k > 0 is a constant. Solve this equation for V in terms of P and T.

a. Determine the rate of change of the volume with respect to the pressure at constant temperature. Interpret the result.

Step 1:

 Relationship between  volume  and pressure

                                 Ideal Gas Law PV = kT,

 

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