Question

Identify the gas filled in the container A and B:

• A. $N_2,Ne$
• B. $He,H_2$
• C. $O_2,Ar$
• D. $Ar,O_2$

Answer 1

The correct option is D $Ar,O_2$

Since the temperature rise and heat supplied to both the container is same.

$Q=n_A{C}_{VA}\Delta T=n_B{C}_{VB}\Delta T$ $\Rightarrow n_A{C}_{VA}=n_B{C}_{VB}-\left(1\right)$

also, $\Delta P_{A}V=n_{A}R\Delta T-\left(2\right)$

and, $\Delta P_{B}V=n_{B}R\Delta T-\left(3\right)$

Dividing $\left(2\right)$ by $\left(3\right)$,

$n_A/n_B=\Delta P_A/\Delta P_B=2.5/1.5=5/3$

$\Rightarrow n_A=5n_B/3$

From equation $\left(1\right)$

$C_{VB}/C_{VA}=5/3=\left(5R/2\right)/\left(3R/2\right)$

$C_{VB}=5R/2$, so $B$ is diatomic.

$C_{VA}=3R/2$, so $A$ is Mono-atomic.

Since $n_A/n_B=5/3-\left(1\right)$

mass of the container is $100g$

Mass of $A$ is $225-100=125$

Let the molecular mass be $M_{A}and{M}_B$

so, $n_A=125/M_A,n_B=60/M_B-\left(2\right)$

From $\left(1\right)and\left(2\right)$

$5M_B=4M_A$

Mass of argon is $40$, oxygen is $32$ which satisfy the above relation.

So, $A$ contains Argon and $B$ contains oxygen.