Two containers of equal volume contain the same gas at the pressure p1 and p2 and absolute temperatures T1 and T2 respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T . The ratio is equal to:

Question

Two containers of equal volume contain the same gas at the pressure p1 and p2 and absolute temperatures T1 and T2 respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T . The ratio is equal to: (A) (p1 T2 + p2 T1/T1 × T2) (B) (p1 T2 + p2 T1/T1 + T2) (C) (1/2) [(p1 T2 + p2 T1/T1 T2)] (D) (p1 T2 - p2 T1/T1 × T2)

Tardigrade Admin · Accepted Answer

For a closed system, the total number of moles remains constant. So p1V=n1RT1 textand p2V=n2RT2 ∴ p(2 V)=(n1 + n2)RT ∴ (p/T)=((n1 + n2)/2 V)R=(1/2)[(P1/T1) + (P2/T2)] ⇒ (p/T)=(1/2)[(p1 T2 + p2 T1/T1 T2)]

Q. Two containers of equal volume contain the same gas at the pressure $p_{1}$ and $p_{2}$ and absolute temperatures $T_{1}$ and $T_{2}$ respectively. On joining the vessels, the gas reaches a common pressure $p$ and a common temperature $T$ . The ratio is equal to:

$\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} \times T _{2}}$

$\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} + T _{2}}$

$\frac{1}{2} [\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} T _{2}}]$

$\frac{p _{1} T _{2} - p _{2} T _{1}}{T _{1} \times T _{2}}$

Q. Two containers of equal volume contain the same gas at the pressure p1​ and p2​ and absolute temperatures T1​ and T2​ respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T . The ratio is equal to:

T1​×T2​p1​T2​+p2​T1​​

T1​+T2​p1​T2​+p2​T1​​

21​[T1​T2​p1​T2​+p2​T1​​]

T1​×T2​p1​T2​−p2​T1​​

For a closed system, the total number of moles remains constant. So p1​V=n1​RT1​andp2​V=n2​RT2​ ∴p(2V)=(n1​+n2​)RT ∴Tp​=2V(n1​+n2​)​R=21​[T1​P1​​+T2​P2​​] ⇒Tp​=21​[T1​T2​p1​T2​+p2​T1​​]

Q. Two containers of equal volume contain the same gas at the pressure $p_{1}$ and $p_{2}$ and absolute temperatures $T_{1}$ and $T_{2}$ respectively. On joining the vessels, the gas reaches a common pressure $p$ and a common temperature $T$ . The ratio is equal to:

$\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} \times T _{2}}$

$\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} + T _{2}}$

$\frac{1}{2} [\frac{p _{1} T _{2} + p _{2} T _{1}}{T _{1} T _{2}}]$

$\frac{p _{1} T _{2} - p _{2} T _{1}}{T _{1} \times T _{2}}$