Find Specific Heat at Constant Pressure of Gas with Molar Mass M

[chaoseverlasting]

Homework Statement

For a gas of molar mass M, Cp/Cv=y. Find specific heat at constant pressure.

The Attempt at a Solution

$$C_p=\frac{Pdv}{ndt}+C_v$$
PV=nRT,
P=constant
$$\frac{P}{n} \frac{dv}{dt}=R$$

Substituting in the above equation:
$$C_p(\frac{y-1}{y})=R$$
$$C_p=\frac{Ry}{y-1}$$

This isn't the answer though, the given answer is $$C_p=\frac{Ry}{M(y-1)}$$. Why? How does M come into the picture?

 

[chaoseverlasting]

Anybody? Please?

 

[Mentz114]

Have you checked your units ? Your proposed answer has the wrong dimensions.

 

[chaoseverlasting]

Where have I made the mistake? What am I doing wrong?