One mole of a monoatomic gas is mixed with th | vedclass

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

Question

(D) The molar specific heat at constant volume for a mixture is given by the formula: $C_{V_{mix}} = \frac{n_1 C_{V_1} + n_2 C_{V_2}}{n_1 + n_2}$.For

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) The molar specific heat at constant volume for a mixture is given by the formula: $C_{V_{mix}} = \frac{n_1 C_{V_1} + n_2 C_{V_2}}{n_1 + n_2}$.For a monoatomic gas,$C_{V_1} = \frac{3}{2} R$ and $n_1 = 1$.For a diatomic gas without vibrational modes,$C_{V_2} = \frac{5}{2} R$ and $n_2 = 3$.Substituting these values into the formula:$C_{V_{mix}} = \frac{1 \cdot (\frac{3}{2} R) + 3 \cdot (\frac{5}{2} R)}{1 + 3} = \frac{\frac{3}{2} R + \frac{15}{2} R}{4} = \frac{\frac{18}{2} R}{4} = \frac{9 R}{4}$.Given that $C_{V_{mix}} = \frac{\alpha^2}{4} R$,we equate the two expressions:$\frac{9 R}{4} = \frac{\alpha^2}{4} R$.This implies $\alpha^2 = 9$,so $\alpha = 3$ (taking the positive value).

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.)

Similar Questions

$N$ 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:

$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture is

The pressure of a mixture of $64 \ g$ of oxygen, $28 \ g$ of nitrogen, and $132 \ g$ of carbon dioxide gases in a closed vessel is $P$. Under isothermal conditions, if the entire oxygen is removed from the vessel, the pressure of the mixture of the remaining two gases is:

$A$ mixture of ideal gases has $2$ moles of $He$,$4$ moles of oxygen $(O_2)$,and $1$ mole of ozone $(O_3)$ at absolute temperature $T$. The internal energy of the mixture is ............. $RT$.

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?

Vedclass Test Series

Exam Paper Generator

Online Exam Module