The ratio of specific heat of a mixture of on | vedclass

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

Question

(B) For a mixture of gases,the adiabatic index $\gamma_{mix}$ is given by $\gamma_{mix} = \frac{C_{P,mix}}{C_{V,mix}} = \frac{n_1 C_{P1} + n_2 C_{P2}}

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

(B) For a mixture of gases,the adiabatic index $\gamma_{mix}$ is given by $\gamma_{mix} = \frac{C_{P,mix}}{C_{V,mix}} = \frac{n_1 C_{P1} + n_2 C_{P2}}{n_1 C_{V1} + n_2 C_{V2}}$.Helium is a monoatomic gas,so $n_1 = 1$,$C_{V1} = \frac{3}{2}R$,and $C_{P1} = \frac{5}{2}R$.Hydrogen is a diatomic gas,so $n_2 = 1$,$C_{V2} = \frac{5}{2}R$,and $C_{P2} = \frac{7}{2}R$.Substituting these values:$C_{V,mix} = \frac{1(\frac{3}{2}R) + 1(\frac{5}{2}R)}{1+1} = \frac{8R/2}{2} = 2R$.$C_{P,mix} = \frac{1(\frac{5}{2}R) + 1(\frac{7}{2}R)}{1+1} = \frac{12R/2}{2} = 3R$.Therefore,$\gamma_{mix} = \frac{3R}{2R} = 1.5$.

The ratio of specific heat of a mixture of one mole of helium and one mole of hydrogen gas will be

Similar Questions

If $\alpha$ moles of a monoatomic gas are mixed with $\beta$ moles of a polyatomic gas and the mixture behaves like a diatomic gas,then [neglect the vibrational mode of freedom]:

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of the mixture at constant volume is $\frac{\alpha^{2}}{4} R \ J/mol \ K$; then the value of $\alpha$ will be $.......$ (Assume that the given diatomic gas has no vibrational mode.)

$N$ moles of a polyatomic gas $(f=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is:

$A$ rigid tank contains $35 \, kg$ of nitrogen at $6 \, atm$. $A$ sufficient quantity of oxygen is supplied to increase the pressure to $9 \, atm$,while the temperature remains constant. The amount of oxygen supplied to the tank is .... $kg$.

One gram of $H_2$ at $27\,^{\circ}C$ is mixed with $16\,g$ of $O_2$ at $37\,^{\circ}C$. The temperature of the mixture is about ....... $^{\circ}C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module