Amonatomic ideal gas has pressure p1 and temperature t1. it is contained in a cylinder of volume v1 with a movable piston, so that it can do work on the outside world. consider the following three-step transformation of the gas: the gas is heated at constant volume until the pressure reaches ap1 (where a> 1). the gas is then expanded at constant temperature until the pressure returns to p1. the gas is then cooled at constant pressure until the volume has returned to v1.
it may be to sketch this process on the pvplane.
how much heat q1 is added to the gas during step 1 of the process?
express the heat added in terms of p1, v1, and a.
how much work w2 is done by the gas during step 2?
express the work done in terms of p1, v1, and a.
how much work w3 is done by the gas during step 3?
if you've drawn a graph of the process, you won't need to calculate an integral to answer this question.
express the work done in terms of p1, v1, and a.

1)

The heat absorbed by the gas can be found by using the 1st law of thermodynamics:

where

is the change in internal energy

Q is the heat absorbed

W is the work done

Since the first process occurs at constant volume, the work done is zero:

So the equation becomes

The change in internal energy is given by

(1)

where

n is the number of moles of the gas, which can be found by using the ideal gas law with the initial conditions of the gas:

(2)

where R is the gas constant,

is the specific heat at constant volume

is the change in temperature. The temperature T2 can calculate again by using the ideal gas law at the new conditions of the gas, after its pressure has reached Ap1:

(3)

Combining (1), (2) and (3), we find:

2)

The work done during an isothermal process is given by:

(4)

where in this case we have:

 (number of moles)

is the constant temperature of the process, found in the previous part

is the final volume, which  can be found again by using the ideal gas law:

is the initial volume

Substituting all the quantities into (4), we find:

3)

Step 3 is an isobatic process (constant pressure), so the work done can be simply calculated as

where:

is the constant pressure of the process

is the final volume

is the initial volume

Substituting into the equation, and keeping in mind that

We find:

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2