HomeworkLib
Problem

Two equal-volume compartments of a box are joined by a thin wall as shown in the figure. T...

Two equal-volume compartments of a box are joined by a thin wall as shown in the figure. The left compartment is filled with 0.0500 mole of helium gas at 500. K, and the right compartment contains 0.0250 mole of helium gas at 250. K. The right compartment also has a piston to which a force of 20.0 N is applied.

a) If the wall between the compartments is removed, what will the final temperature of the system be?

b) How much heat will be transferred from the left compartment to the right compartment?

c) What will be the displacement of the piston due to this transfer or heat?

d) What fraction of the heat will be converted into work?

Step-by-Step Solution

Solution 1
Step #1 of 9

THINK:

In the given situation, the heat will be transferred from the system 1 to 2, since the system 1 is at higher temperature with the net heat flow of zero.

SKETCH:

The given system is shown below.

Step #2 of 9

RESEARCH:

Work done by the heat transfer,

Change in internal energy is

Step #3 of 9

CALCULATE:

Number of moles of helium in the left compartment,

Temperature at the left compartment is

Number of moles of helium in the right compartment,

Temperature at the right compartment is

Force on the piston of right compartment,

Step #4 of 9

(a) If the wall between the compartments is removed, then the final temperature of the

system is obtained as follows.

From the above two equations, we get

Step #5 of 9

(b) Heat transferred from left compartment to right compartment:

Step #6 of 9

(c) Displacement of the piston due to the heat:

Step #7 of 9

(d) The fraction of the heat will be converted into work:

Step #8 of 9

ROUND:

We report our result to three significant figures.

(a) Final temperature is

(b) Heat transferred is

Step #9 of 9
(c) Displacement of the piston is

(d) Fraction of the heat transferred is

Add your Solution
Textbook Solutions and Answers Search
Solutions For Problems in Chapter 20
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
Recent Solutions