Log In Start studying!
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q. 49

Expert-verified
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 545

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

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

Step by Step Solution

Step 1: Given Information (Part a)

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

Step 4: Given Information (Part b)

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,

Step 7: Given Information (Part c)

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.

Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.