relation between cp and cv ?
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Heat Capacity - Relationship Between Cp and Cv for Ideal Gas -
Thus, the change in temperature is proportional to the heat transfer. The formula q = n C ∆T represents the heat q required to bring about a ∆T difference in temperature of one mole of any matter. ... In this article, we will discuss two types of molar heat capacity – CP and CV and derive a relationship between Cp and Cv.
Thus, the change in temperature is proportional to the heat transfer. The formula q = n C ∆T represents the heat q required to bring about a ∆T difference in temperature of one mole of any matter. ... In this article, we will discuss two types of molar heat capacity – CP and CV and derive a relationship between Cp and Cv.
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From the equation q = n C ∆T, we can say:
At constant pressure P, we have
qP = n CP∆T
This value is equal to the change in enthalpy, that is,
qP = n CP∆T = ∆H
Similarly, at constant volume V, we have
qV = n CV∆T
This value is equal to the change in internal energy, that is,
qV = n CV∆T = ∆U
We know that for one mole (n=1) of an ideal gas,
∆H = ∆U + ∆(pV ) = ∆U + ∆(RT) = ∆U + R ∆T
Therefore, ∆H = ∆U + R ∆T
Substituting the values of ∆H and ∆U from above in the former equation,
CP∆T = CV∆T + R ∆T
CP = CV + R
CP – CV = R
At constant pressure P, we have
qP = n CP∆T
This value is equal to the change in enthalpy, that is,
qP = n CP∆T = ∆H
Similarly, at constant volume V, we have
qV = n CV∆T
This value is equal to the change in internal energy, that is,
qV = n CV∆T = ∆U
We know that for one mole (n=1) of an ideal gas,
∆H = ∆U + ∆(pV ) = ∆U + ∆(RT) = ∆U + R ∆T
Therefore, ∆H = ∆U + R ∆T
Substituting the values of ∆H and ∆U from above in the former equation,
CP∆T = CV∆T + R ∆T
CP = CV + R
CP – CV = R
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