Two flasks R and S of volume V1 and V2 contain same gas at pressure P1 and P2 respectively at the same temperature. Pressure of the gas when the flasks R and S are connected by a tube of negligible volume is

Question

Two flasks R and S of volume V1 and V2 contain same gas at pressure P1 and P2 respectively at the same temperature. Pressure of the gas when the flasks R and S are connected by a tube of negligible volume is (A) (P1 V1+P2 V2/V1+V2) (B) (P1 V1+P2 V2/2(V1+V2)) (C) (P1 V2+P2 V1/V1+V2) (D) ((P1+P2)(V1+V2)/(V1+2 V2))

Tardigrade Admin · Accepted Answer

Number of moles of gas in two flasks are n1=(P1 V1/R T) and n2=(P2 V2/R T) ∵ n=n1+n2 ∴ P=((n1+n2) R T/V1+V2) =(P1 V1+P2 V2/V1+V2)

Q. Two flasks $R$ and $S$ of volume $V_{1}$ and $V_{2}$ contain same gas at pressure $P_{1}$ and $P_{2}$ respectively at the same temperature. Pressure of the gas when the flasks $R$ and $S$ are connected by a tube of negligible volume is

$\frac{P _{1} V _{1} + P _{2} V _{2}}{V _{1} + V _{2}}$

$\frac{P _{1} V _{1} + P _{2} V _{2}}{2 ( V _{1} + V _{2} )}$

$\frac{P _{1} V _{2} + P _{2} V _{1}}{V _{1} + V _{2}}$

$\frac{( P _{1} + P _{2} ) ( V _{1} + V _{2} )}{( V _{1} + 2 V _{2} )}$

Number of moles of gas in two flasks are
$n_{1} = \frac{P _{1} V _{1}}{RT}$ and
$n_{2} = \frac{P _{2} V _{2}}{RT}$
$∵ n = n_{1} + n_{2}$
$∴ P = \frac{( n _{1} + n _{2} ) RT}{V _{1} + V _{2}}$
$= \frac{P _{1} V _{1} + P _{2} V _{2}}{V _{1} + V _{2}}$

Q. Two flasks R and S of volume V1​ and V2​ contain same gas at pressure P1​ and P2​ respectively at the same temperature. Pressure of the gas when the flasks R and S are connected by a tube of negligible volume is

V1​+V2​P1​V1​+P2​V2​​

2(V1​+V2​)P1​V1​+P2​V2​​

V1​+V2​P1​V2​+P2​V1​​

(V1​+2V2​)(P1​+P2​)(V1​+V2​)​