Two cylinder having `m_(1)g` and `m_(2)g` of a gas at pressure `P_(1)` and `P_(2)` respectively are put in cummunication with each other, temperature remaining constant. The common pressure reached will be

Options

A. `(m_(1)m_(2)P_(2))/(P_(2)m_(1)+P_(1)m_(2))`
B. `(P_(1)P_(2)m_(1))/(P_(2)m_(1)+P_(1)m_(2))`
C. `(m_(1)m_(2)(P_(1)+P_(2)))/(P_(2)m_(1)+P_(1)m_(2))`
D. `(P_(1)P_(2)(m_(1)+m_(2)))/(P_(2)m_(1)+P_(1)m_(2))`

Answer

D

Explanation

As temperature is constant
`P_(1)V_(1) = ((m_1)/(M))RT`..(i)
`P_(2)V_(2) = ((m_2)/(M))RT` ..(ii)
When both cylinder are connected
`P(V_(1)+V_(2)) = ((m_(1)+m_(2)))/(M) RT` ..(ii)
From (i), (ii) and (iii)
`P[(m_1)/(M)(RT)/(p_1)+(m_2)/(M)(RT)/(p_2)]=((m_(1)+m_(2))/(m) RT`
`implies P[(m_1)/(P_1)+(m_2))/(P_2)] = (m_(1)+m_(2))`
Hence, `P = (P_(1)P_(2)(m_(1)+m_(2)))/((m_(1)P_(2)+m_(2)P_(1))`.