Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is

Question

Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is (A)  P  (B)  (P/2)  (C)  4 P  (D)  2 P

Tardigrade Admin · Accepted Answer

(p1 V1/T1)=(pmix × Vmix/Tmix) Here, T1=Tm i x=T V1=V+V Vmix=V ∴ (p × 2 V/T)=(pmix × V/T) ⇒ pmix=2 p

Q. Two monoatomic ideal gases $A$ and $B$ occupying the same volume $V$ , are at the same temperature $T$ and pressure $p$ . If they are mixed, the resultant mixture has volume $V$ and temperature $T$ . The pressure of the mixture is

$P$

$\frac{P}{2}$

$4 P$

$2 P$

$\frac{p _{1} V _{1}}{T _{1}} = \frac{p _{mi x} \times V _{mi x}}{T _{mi x}}$
Here, $T_{1} = T_{mi x} = T$
$V_{1} = V + V$
$V_{mi x} = V$
$∴ \frac{p \times 2 V}{T} = \frac{p _{mi x \times V}}{T}$
$\Rightarrow p_{mi x} = 2 p$

Q. Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is

P

2P​

4P

2P

T1​p1​V1​​=Tmix​pmix​×Vmix​​ Here, T1​=Tmix​=T V1​=V+V Vmix​=V ∴Tp×2V​=Tpmix×V​​ ⇒pmix​=2p

Q. Two monoatomic ideal gases $A$ and $B$ occupying the same volume $V$ , are at the same temperature $T$ and pressure $p$ . If they are mixed, the resultant mixture has volume $V$ and temperature $T$ . The pressure of the mixture is

$P$

$\frac{P}{2}$

$4 P$

$2 P$

$\frac{p _{1} V _{1}}{T _{1}} = \frac{p _{mi x} \times V _{mi x}}{T _{mi x}}$
Here, $T_{1} = T_{mi x} = T$
$V_{1} = V + V$
$V_{mi x} = V$
$∴ \frac{p \times 2 V}{T} = \frac{p _{mi x \times V}}{T}$
$\Rightarrow p_{mi x} = 2 p$