A gaseous mixture consists of 4 g oxygen and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a gas mixture,the adiabatic index $\gamma_{	ext{mix}}$ is given by $\gamma_{	ext{mix}} = \frac{C_{p(	ext{mix})}}{C_{V(	ext{mix})}}$.Using

Vedclass · Accepted Answer

$\frac{47}{29}$

Vedclass · Answer

(C) For a gas mixture,the adiabatic index $\gamma_{	ext{mix}}$ is given by $\gamma_{	ext{mix}} = \frac{C_{p(	ext{mix})}}{C_{V(	ext{mix})}}$.Using the formula for mixture properties: $\gamma_{	ext{mix}} = \frac{n_1 C_{p1} + n_2 C_{p2}}{n_1 C_{V1} + n_2 C_{V2}}$.For oxygen $(O_2)$,which is diatomic: $n_1 = \frac{4 \ g}{32 \ g/mol} = \frac{1}{8} \ mol$. $C_{p1} = \frac{7}{2}R$,$C_{V1} = \frac{5}{2}R$.For helium (He),which is monatomic: $n_2 = \frac{4 \ g}{4 \ g/mol} = 1 \ mol$. $C_{p2} = \frac{5}{2}R$,$C_{V2} = \frac{3}{2}R$.Substituting these values into the formula:$\gamma_{	ext{mix}} = \frac{(\frac{1}{8} 	imes \frac{7}{2}R) + (1 	imes \frac{5}{2}R)}{(\frac{1}{8} 	imes \frac{5}{2}R) + (1 	imes \frac{3}{2}R)}$$\gamma_{	ext{mix}} = \frac{\frac{7}{16} + \frac{5}{2}}{\frac{5}{16} + \frac{3}{2}} = \frac{\frac{7+40}{16}}{\frac{5+24}{16}} = \frac{47}{29}$.

$A$ gaseous mixture consists of $4 \ g$ oxygen and $4 \ g$ of helium. The ratio $\frac{C_p}{C_V}$ of the mixture is ($C_p$ and $C_V$ are molar specific heats of the mixture at constant pressure and at constant volume respectively).

Similar Questions

When one mole of monatomic gas is mixed with one mole of a diatomic gas,then the equivalent value of $\gamma$ for the mixture will be (vibration mode neglected).

$A$ container holds $8 \, g$ of $O_2$ and $7 \, g$ of $N_2$ at a pressure of $10 \, atm$. If $O_2$ is removed,the pressure becomes ... $atm$.

$N_1$ molecules of a gas at temperature $T_1$ are mixed with $N_2$ molecules at temperature $T_2$. The resulting temperature of the mixture gas is

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be:

$A$ cylinder consists of a gas mixture of helium and oxygen. If the mass of helium is $4 \,g$ and the mass of oxygen is $32 \,g$, then the ratio of specific heat of the mixture $\left(C_p / C_V\right)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module