Two identical containers contain equal amounts of the same ideal gas at a temperature T0 and pressure P0 . Now the two containers are connected through a tube having negligible volume and one container is heated to 2T0 while the other is kept at T0 . The final common pressure will be

Question

Two identical containers contain equal amounts of the same ideal gas at a temperature T0 and pressure P0 . Now the two containers are connected through a tube having negligible volume and one container is heated to 2T0 while the other is kept at T0 . The final common pressure will be (A) (2 P0/3) (B) (4 P0/3) (C) (P0/3) (D) 2P0

Tardigrade Admin · Accepted Answer

(P0 V/R T0)+(P0 V/R T0)=(P V/R T0)+(P V/R 2 T0) 2P0=P+(P/2) 2P0=(3 P/2) P=(4 P0/3)

$\frac{2 P _{0}}{3}$

$\frac{4 P _{0}}{3}$

$\frac{P _{0}}{3}$

$2 P_{0}$

$\frac{P _{0} V}{R T _{0}} + \frac{P _{0} V}{R T _{0}} = \frac{P V}{R T _{0}} + \frac{P V}{R 2 T _{0}}$
$2 P_{0} = P + \frac{P}{2}$
$2 P_{0} = \frac{3 P}{2}$
$P = \frac{4 P _{0}}{3}$

Q. Two identical containers contain equal amounts of the same ideal gas at a temperature T0​ and pressure P0​ . Now the two containers are connected through a tube having negligible volume and one container is heated to 2T0​ while the other is kept at T0​ . The final common pressure will be

32P0​​

34P0​​

3P0​​

2P0​

RT0​P0​V​+RT0​P0​V​=RT0​PV​+R2T0​PV​ 2P0​=P+2P​ 2P0​=23P​ P=34P0​​

$\frac{2 P _{0}}{3}$

$\frac{4 P _{0}}{3}$

$\frac{P _{0}}{3}$

$2 P_{0}$

$\frac{P _{0} V}{R T _{0}} + \frac{P _{0} V}{R T _{0}} = \frac{P V}{R T _{0}} + \frac{P V}{R 2 T _{0}}$
$2 P_{0} = P + \frac{P}{2}$
$2 P_{0} = \frac{3 P}{2}$
$P = \frac{4 P _{0}}{3}$