How does the constant‑volume molar specific heat of the gas, Cp, relate to the constant‑pressure molar specific heat, Cp?
This was asked as part of the feedback for Achieve Week 4 question 18, but I'm not sure the answer.
Relationship Between Cv and Cp
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Re: Relationship Between Cv and Cp
I think that Cp = Cv + R but does anyone know the reason for this? Thanks!
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Re: Relationship Between Cv and Cp
Hi Lawrence,
Like Anthony mentioned, Cp = Cv + R is the relationship between Cv and Cp. A good way to reason this is through the statement that Cp will always be greater than Cv. Since systems at a constant pressure can expand with an increase in temperature, work is done by the system through expansion—meaning the system requires more energy to raise the temperature, hence the need for a greater Cp value. Conversely, in a system at a constant volume, temperature increases will lead to increases in pressure, which do not correlate to work being done by the system. No work being done will lead to a lower Cv value. Hope this helps!
Like Anthony mentioned, Cp = Cv + R is the relationship between Cv and Cp. A good way to reason this is through the statement that Cp will always be greater than Cv. Since systems at a constant pressure can expand with an increase in temperature, work is done by the system through expansion—meaning the system requires more energy to raise the temperature, hence the need for a greater Cp value. Conversely, in a system at a constant volume, temperature increases will lead to increases in pressure, which do not correlate to work being done by the system. No work being done will lead to a lower Cv value. Hope this helps!
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