Two containers of equal volume contain the same gas at pressures 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 (P/T) is

Question

Two containers of equal volume contain the same gas at pressures 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 (P/T) is (A) (P1/T1)+(P2/T2) (B) (1/2)[(P1/T1)+(P2/T2)] (C) (P1 T2+P2 T1/T1+T2) (D) (P1 T2-P2 T1/T1-T2)

Tardigrade Admin · Accepted Answer

For a closed system, the total mass of gas or the number of moles remains constant. Let

n_{1}

and

n_{2}

be number of moles of gas in container 1 and container 2 respectively.

P_{1} V = n_{1} R T_{1}

or

n_{1} = \frac{P _{1} V}{R T _{1}} \dots

(i)

P_{2} V = n_{2} R T_{2}

or

n_{2} = \frac{P _{2} V}{R T _{2}} \dots

(ii)

P (2 V) = (n_{1} + n_{2}) RT \dots

(iii)
Substituting the values of

n_{1}

and

n_{2}

in equation (iii), we get

P (2 V) = (\frac{P _{1} V}{R T _{1}} + \frac{P _{2} V}{R T _{2}}) RT

or

\frac{P}{T} = \frac{1}{2} (\frac{P _{1}}{T _{1}} + \frac{P _{2}}{T _{2}})

Q. Two containers of equal volume contain the same gas at pressures $P_{1}$ 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 $\frac{P}{T}$ is

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

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

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

$\frac{P _{1} T _{2} - P _{2} T _{1}}{T _{1} - T _{2}}$

Q. Two containers of equal volume contain the same gas at pressures 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 TP​ is

T1​P1​​+T2​P2​​

21​[T1​P1​​+T2​P2​​]

T1​+T2​P1​T2​+P2​T1​​

T1​−T2​P1​T2​−P2​T1​​

Q. Two containers of equal volume contain the same gas at pressures $P_{1}$ 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 $\frac{P}{T}$ is

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

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

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

$\frac{P _{1} T _{2} - P _{2} T _{1}}{T _{1} - T _{2}}$