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Old Feb 17th 2014, 07:55 AM   #1
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Heat equation

I understand that dq = du + dw. However, there is a version of this equation that goes like this: dq = c_v * dT + pdV
I don't understand why the pdV term isn't zero since we are considering volume to be constant. Isn't that what using c_v implies? Please explain. Thank you in advance.
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Old Feb 18th 2014, 05:42 AM   #2
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Such is the nature of partial differential equations. The first term with C_v assumes constant volume, and the second term PdV assumes constant temperature. In essence the equation adds the two effects of changing volume and temp as separate terms.

Last edited by ChipB; Feb 18th 2014 at 09:20 AM.
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Old Feb 19th 2014, 01:15 PM   #3
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This is always confusing...

Hello Princess,

Many students get confused by c<sub>v</sub>.
Here is the short answer.

c<sub>v</sub> is a substance property.
Values of c<sub>v</sub> can be (as indicated) determined
by a process during which "v" is held constant. Also c<sub>v</sub>
can be calculated.

However, once c<sub>v</sub> is determined at a state, the value belongs to that state and has that value no matter what path is taken through it.

Hope this helps... I'm out to dinner... no time.

Here are some problems perhaps of interest you...

http://www.thermospokenhere.com/tsh/preview.php

TSH
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