Two chamber containing m1 and m2 grams of a gas at pressures P1 and P2 respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

Question

Two chamber containing m1 and m2 grams of a gas at pressures P1 and P2 respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be (A) (P1P2(m1 + m2)/P2m1 + P1m2) (B) (P1P2m1 /P2m1 + P1m2) (C) (m1m2(P1 + P2) /P2m1 + P1m2) (D) (m1m2 P2 /P2m1 + P1m2)

Tardigrade Admin · Accepted Answer

According to Boyles law, PV = kT (a constant) or P (m/ρ) = kT or ρ = (Pm/kT) or ρ = (P/K) (where (kT/m) = K a constant) So, ρ1= (P1/K) and V1 = (m1/ρ1) = (m1/P1 /K) = (Km1/P1) Similarly, V2 = (Km2/P2) Total volume =V1 + V2 = K ((m1/P1) + (m2/P2)) Let P be the common pressure and ρ be the common density of mixture. Then. ρ = (m1 + m2/V1 + V2) = (m1 + m2/K((m1)P1 + (m2)P2) ∴ P = Kρ = (m1 + m2/(m1)P1 + (m2)P2 = (P1P2(m1+ m2)/(m1P2 + m2P1))

Q. Two chamber containing $m_{1}$ and $m_{2}$ grams of a gas at pressures $P_{1}$ and $P_{2}$ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

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

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

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

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

Q. Two chamber containing m1​ and m2​ grams of a gas at pressures P1​ and P2​ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

P2​m1​+P1​m2​P1​P2​(m1​+m2​)​

P2​m1​+P1​m2​P1​P2​m1​​

P2​m1​+P1​m2​m1​m2​(P1​+P2​)​

P2​m1​+P1​m2​m1​m2​P2​​

Q. Two chamber containing $m_{1}$ and $m_{2}$ grams of a gas at pressures $P_{1}$ and $P_{2}$ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

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

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

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

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