For an ideal gas, (Cp, m/CV, m)=r. The molecular mass of the gas is M, its specific heat capacity at constant volume is

Question

For an ideal gas, (Cp, m/CV, m)=r. The molecular mass of the gas is M, its specific heat capacity at constant volume is (A)  (rR/M(r-1))  (B)  (rRM/r-1)  (C)  (M/R(r-1))  (D)  (R/M(r-1))

Tardigrade Admin · Accepted Answer

As (Cp, m/CV, m)=r and Cp, m-CV, m=R ∴ CV,m=(R/r-1) CV, m=(CV/n) and CV=m⋅ CV ∴ (R/r-1)=(m⋅ CV/m)× M ∴ CV=(R/(r-1) M)

Q. For an ideal gas, $\frac{C _{p} , m}{C _{V} , m} = r .$ The molecular mass of the gas is M, its specific heat capacity at constant volume is

$\frac{r R}{M ( r - 1 )}$

$\frac{r RM}{r - 1}$

$\frac{M}{R ( r - 1 )}$

$\frac{R}{M ( r - 1 )}$

As $\frac{C _{p} , m}{C _{V} , m} = r$ and $C_{p, m} - C_{V, m} = R$ $∴$ $C_{V, m} = \frac{R}{r - 1}$ $C_{V, m} = \frac{C _{V}}{n}$ and $C_{V} = m \cdot C_{V}$ $∴$ $\frac{R}{r - 1} = \frac{m \cdot C _{V}}{m} \times M$ $∴$ $C_{V} = \frac{R}{( r - 1 ) M}$

Q. For an ideal gas, CV​,mCp​,m​=r. The molecular mass of the gas is M, its specific heat capacity at constant volume is

M(r−1)rR​

r−1rRM​

R(r−1)M​

M(r−1)R​