Calculating Cp for Ideal Gases using Thermodynamic Relationships

[Rongeet Banerjee]

Homework Statement

Is Meyers equation :
Cp - Cv =R always valid?

Relevant Equations

Cp=Cv +R

In this particular Question according to Meyer's formula,the value of Cp should be (8.314+5) i.e. 13.314 .But that option is missing.
There is another approach to this problem by finding the Adiabatic Coefficient and then finding Cp.I have no problem with that approach.
But my initial doubt still remains.

 

[Andrew Mason]

Homework Statement:: Is Meyers equation :
Cp - Cv =R always valid?
Relevant Equations:: Cp=Cv +R

View attachment 264333
In this particular Question according to Meyer's formula,the value of Cp should be (8.314+5) i.e. 13.314 .But that option is missing.
There is another approach to this problem by finding the Adiabatic Coefficient and then finding Cp.I have no problem with that approach.
But my initial doubt still remains.

Cp = Cv + R is true only for an ideal gas. However, the volume occupied by one mole of gas at a certain temperature and pressure (NTP in this case) is the same for ideal and real gases. I think you are expected to determine $\gamma$ from the speed of sound and determine Cp from that.

AM

 

[Rongeet Banerjee]

Thanks

 

[etotheipi]

Just to provide some justification: For any gas, you have $C_V = \left(\frac{\partial U}{\partial T} \right)_V$ and $C_p = \left(\frac{\partial H}{\partial T} \right)_p$. Now $$H = U + pV \implies \left(\frac{\partial H}{\partial T} \right)_p = \left(\frac{\partial U}{\partial T} \right)_p + p \left(\frac{\partial V}{\partial T} \right)_p$$For an ideal gas, you have $C_V = \left(\frac{\partial U}{\partial T} \right)_V = \left(\frac{\partial U}{\partial T} \right)_p$. Furthermore for an ideal gas, $V = \frac{nRT}{p} \implies p \left(\frac{\partial V}{\partial T} \right)_p = nR$. Hence we finally obtain $$C_p = C_V + nR$$