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Old Dec 3rd 2017, 08:44 PM   #1
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Ideal Gases as a model/ entropy where to start.

(a) Using ideal gases as a model, show that the increase of entropy of n moles of a gas heated at constant pressure from a temperature T1 to a temperature T2 is
$\displaystyle ΔS = nCpln(T2/T1) $

(b) Show that the increase of entropy of a gas heated at constant volume from a temperature T1 to a temperature T2 is $\displaystyle ΔS = nCvln(T2/T1) $

I am aware that I am supposed to show some work but I do not have a clue where to start this problem. A point in the right direction(equations to use) or a walk through would be greatly appreciated. Thank you.
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Old Dec 5th 2017, 07:59 AM   #2
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For part a)

Hint 1: The definition of entropy is

$\displaystyle dS = \frac{dQ}{T}$

Hint 2: When an ideal gas is heated at constant pressure, some of the energy will go into internal energy and some will be used to expand the gas. The proportion that goes into internal energy is

$\displaystyle dQ = m c_p dT$

part b)

Hint: At constant volume, all of the heat goes into internal energy because the gas doesn't expand, so no work is done. What variables change in the above formulae when you have heat transfer at constant volume?
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