In: Physics

An ideal monoatomic gas is separated into two volumes
V1 and V2 by means of

of a diathermic piston, such that each volume contains N atoms and
both parts are

they find at the same temperature T0. The complete system is
isolated from the

exterior by means of insulating walls.

The piston is externally manipulated reversibly until the two gases
are

they find in thermodynamic equilibrium one with the other.

The purpose is to find the final temperature and the work done, or
by the system, or

in the surroundings.

To answer this problem, follow the steps described below and
answer

the questions that are asked:

a) What is the name of the type of process described? Show
that

ΔS1 = -ΔS2

where ΔS1 and ΔS2 are the changes in the entropies of the two
gases.

b) Write the equilibrium conditions in the final state and find the
final volumes

On each side.

c) Find the final temperature. (Hint: Use the First Law on each
side and the

result of subsection a)).

d) Find the total work due to the manipulation of the piston. Does
the system do work

Or does the external agent do work on the system? Explain

a) The process takes place in a reversible way while being thermally isolated from its surrounding (and not heat transfer into the system). This is by definition adiabatic process. We are assuming a massless piston here.

This means heat moves from one chamber to the other only via the diathermic wall. that is:

Having the differentials are defined appropriately, dived both sides by instantaneous T. They will be same on both sides since the wall conducts heat, We reach the definition of entropy, i.e.:

This, upon integration, gives your result.

b) You have the same gas of equal amount on both sides, the walls conduct heat and the piston makes sure the pressures stay same on both sides so as to reach the final thermal equilibrium. So, since P, n, R, T are same pn both sides, you have to have same V on both sides too such that V on each sides would be .

c) It is not clear from your question, but I am assuming you had temperature on both sides to start with. Upon reaching equilibrium, you have equal volumes.

Now using first law: .

Since the temperature did not change throughout and neither did any heat went into the system and the temperature did not change too (since the walls are diathermic) and you started with equal T.

So final temperature: .

d) The manipulation of the system extracted a positive work out of it. Which was entirely due to the equilibration of the pressures.

You can use the formula for work done for adiabatic processes as given here: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html

(a) If V1,V2⊂V show that (V2^⊥)⊂(V1^⊥) implies V1⊂V2
(b) If V1,V2⊂V , show that (V1+V2)^⊥=(V1^⊥)∩(V2^⊥) where we
write V1+V2 to be the subspace of V spanned by V1 and V2 .

How is Avogadro's principle (n1/v1=n2/v2) derived from the ideal
gas law. Can you show me the algebraic steps?

Consider a monoatomic ideal gas of N moles in a gas cylinder
eqilibrated at temperature T1 and pressure P1 by a mass placed on
the piston. Upon removal of the mass , the gas reaches a new
eqilibrium pressure P2 (<P1). Calculate the amount of work done
by the gas on the surroundings for the following processes.
( You must express your answer in terms of the given
variables.)
1. a nonquasistatic isothermal process (sudden removal of the
mass)
2....

if {v1,v2,v3} is a linearly independent set of vectors, then
{v1,v2,v3,v4} is too.

Four moles of a monoatomic ideal gas in a cylinder at 27 degrees
Celsius is expanded at constant pressure equal to 1 atm until its
volume is doubled.
a) What is the change in internal energy?
b) How much work was done by the gas in the process?
c) How much heat was transferred to the gas?

(A) Derive the canonical partition function for a monoatomic
ideal gas. (B) Using the partition function, derive the entropy for
a monoatomic gas.
can you help me with detailed explanations

One mole of a monoatomic, ideal gas at initial pressure
P0 and volume V0 goes to
2P0 a) along the path PV = constant,
and b) at constant volume. Find the heat added to the gas in each
case.

An engine that operates by means of an ideal diatomic ideal gas
in a piston with 2.70 moles of gas. The gas starts at point A with
3x103 Pa of pressure and 2.5x10-2 m3. To get from B from A, it is
expanded by an isobaric process to double the initial volume. From
B to C it expands adiabatically until it reaches three times the
volume in A. From C to D the pressure decreases without changing
the volume and...

v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19].
Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2 is
not a scalar multiple of either v1 or v3 and v3 is not a scalar
multiple of either v1 or v2. Does it follow that every vector in R3
is in span{v1,v2,v3}?

V1
V2
V3
V4
V1
1.0
V2
.27
1.0
V3
-.13
.65
1.0
V4
.20
-.15
-.72
1.0
IN THIS EXERCISE, YOU WILL SEE A CORRELATION MATRIX. EXAMINE THE
MATRIX AND ANSWER THE QUESTIONS THAT FOLLOW.
1. Which two variables have the strongest (largest)
relationship?
2. Which two variables have the weakest (smallest)
relationship?
3. Which two variables have the strongest positive
relationship?
4. which two variables have the stronger negative
relationship?
5. Which two variables have the weakest positive...

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- What is the treatment for schzophrenia condition? How was this disorder treated in the past? Has...
- Which of these are a case for Cultural Relativism? 1. Different societal contexts demand different moral...
- Annuity You are going to borrow money from the bank. But when considering your income, you...
- As you will learn, working in groups is no easy task! Hopefully, you will master some...
- An agronomist is conducting a field experiment to identify the best management practice for minimizing spread...
- What’s a firm’s market value? What are some factors driving a firm’s market value?
- Create the following positions based upon a job analysis: Mailroom clerk: Entry level for a long-term...

ADVERTISEMENT