GREPhysics.NET
GR | # Login | Register
   
  GR9677 #73
Problem
GREPhysics.NET Official Solution    Alternate Solutions
This problem is still being typed.
Thermodynamics}Adiabatic Work

One should recall the expression for work done by an ideal gas in an adiabatic process. But, if not, one can easily derive it from the condition given in the problem, viz., PV^\gamma =C \Rightarrow P=C/V^\gamma.

Recall that the definition of work is W=\int PdV =\int_{V_1}^{V_2} C dV/V^\gamma =\left.-\frac{1}{\gamma-1} C/V^{\gamma -1} \right|_{V_1}^{V_2}, which when one plugs in the endpoint limits, becomes choice (C).

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
There are no Alternate Solutions for this problem. Be the first to post one!
Comments
archard
2010-05-30 13:30:19
Once you see that you have an integrand \frac{dV}{V^\gamma}, you can pretty much bet that the answer is C since it's the only one with a \1-\gamma in the denominator.NEC
Inri
2010-04-09 23:29:04
You can immediately eliminate (D) and (E) by knowing that the numerator can't depend that way on gamma, as it produce the wrong units for anything but gamma = 0. You can immediately eliminate (A) by knowing that the work depends on the initial pressure and volume.

You can eliminate (B) by knowing that the sum of the pressures shouldn't affect the final work (though the difference might).

That leaves option (C).

Fortunately, the integral is not too difficult and in this problem you only need to get so far as the constant (\gamma - 1) or (1 - \gamma) as there is only one option with that constant.
NEC
a19grey2
2008-10-30 21:07:21
If we plug in C's dependence on V later in the problem, why can we ignore this dependence when doing the integral?
gt2009
2009-07-03 12:35:10
C is a constant so you can pull it out of the integral. It is not ignoring anything.
NEC
physicsisgod
2008-10-30 15:07:48
It took me a minute to realize how \frac{C}{V^{\gamma -1}} = PV, so in case anyone else has this problem:

\frac{C}{V^{\gamma -1}} = \frac{C}{V^\gamma V^{-1}} = \frac{C}{V^\gamma} V= PV

Tada! Thanks, ETS, for putting the correct answer in the most laborious form possible!
AER
2009-03-31 17:15:29
Thankfully, once you get the 1-\gamma factor, you're done.
sullx
2009-11-03 18:54:33
Yeah. After I saw the 1-\gamma factor I was confident of C.
NEC

Post A Comment!
Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...


ShoutMix chat widget

1GHz Smartphone for 1 cent - best deal on a Samsung Galaxy Phone

Millions of Books, Journals and Articles

Find Scholarships Today!

Search FastWeb see Green!

SL Button 125

Free 3D Virtual World. Largest User-Created Fantasy World. Don't Play, Experience. Join Now!

Bored, got time to kill, and want to earn micro-cash by mindlessly clicking on links? Join CrownGPT. Click Offers. Click the Paid to Click button... then click to your heart's delight.

90% Off + FREE SHIPPING!

FREE 3D Virtual World Chat - Join Second Life Today!