Question

For a certain gas , 7 Cp = 9 Cv, Then its Cv is equal to​

Answer 1

• Here, the relation between Cp and Cv  is given as

7 Cp = 9 Cv   -----  (1)

• We, also know a relation between Cp, Cv and R , which we will use to find the value of Cp.

Cp - Cv = R    ------ (2)

This is called the Mayer's relation.

• In order to find Cv, we will first get the value of Cp in terms of Cv.

so, from equation (1)

$Cp$ = $\frac{9}{7} Cv$

• Now, we will substitute the value in equation (2)

$\frac{9}{7} Cv - Cv = R$

$9Cv - 7Cv= 7R\\2Cv=7R\\Cv= \frac{7}{2} R$

Putting the value of R= 8.314

Cv = 29.099

   

Answer 2

7 Cp = 9 Cv ——- is the relationship between Cp and Cv in this case (1)

We also know a relationship between Cp, Cv, and R, which we'll utilise to calculate Cp's value.

Cp - Cv = R ------ (2)

The Mayer's connection is the name for this relationship.

To find Cv, we must first determine Cp's value in terms of Cv.

as a result of equation (1)

=$\begin{array}{l}\frac{9}{7} C v-C v=R \\9 C v-7 C v=7 R \\2 C v=7 R \\C v=\frac{7}{2} R\end{array}$

Now we'll change the value in equation (2)

Using R= 8.314 as an example

Cv = 29.099