Q. 49

Expert-verifiedFound in: Page 545

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

Amount of gas

Temperature

Pressure

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

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

(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

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

Below a sketch of such a graph is given:

Therefore the graph of has been shown.

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