Q. 49

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Found in: Page 545

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

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

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# of gas are at and a pressure of . How much work must be done on the gas to compress it to one-third of its initial volume at (a) constant temperature and (b) constant pressure? (c) Show both processes on a single diagram.

a) Amount of work must be done on the gas to compress it to one-third of its initial volume at constant temperature is

b) Amount of work must be done on the gas to compress it to one-third of its initial volume at constant pressure is

c) The diagrammatic representation of diagram is

See the step by step solution

Amount of gas

Temperature

Pressure

## Step 2: Explanation (Part a)

In an isothermal process, the work is given by

We know that the final volume is one third of the initial volume; substituting that and the other information we are given, we have

## Step 3: Final Answer (Part a)

Hence, the amount of work must be done on the gas to compress it to one-third of its initial volume at constant temperature is

Amount of gas

Temperature

Pressure

## Step 5: Explanation (Part b)

(b) In an isobaric process the work is given by

In our case, knowing the relation between the initial and final volumes, we have

We therefore need to find the initial volume from the state equation, we have

We can therefore substitute in the expression for the work and find that

## Step 6: Final Answer (Part b)

In our numerical case, we will have

Amount of work must be done on the gas to compress it to one-third of its initial volume at constant pressure is,

Amount of gas

Temperature

Pressure

## Step 8: Explanation (Part c)

Below a sketch of such a graph is given:

## Step 9: Final Answer (Part c)

Therefore the graph of has been shown.

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