Question

Two closed vessels of equal volume containing air at pressure $P _ { 1 }$ and temperature $T _ { 1 }$ are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at $T _ { 1 }$ and that in the other at $T _ { 2 }$, what will be the pressure in the vessels.

• A. $\frac { 2 P _ { 1 } T _ { 1 } } { T _ { 1 } + T _ { 2 } }$
• B. $\frac { T _ { 1 } } { 2 P _ { 1 } T _ { 2 } }$
• C. $\frac { 2 P _ { 1 } T _ { 2 } } { T _ { 1 } + T _ { 2 } }$
• D. $\frac { 2 P _ { 1 } } { T _ { 1 } + T _ { 2 } }$

Answer 1

Answer: (C)

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

Answer 2

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

$\frac { 2 P _ { 1 } } { T _ { 1 } } = P \left( \frac { T _ { 1 } + T _ { 2 } } { T _ { 1 } T _ { 2 } } \right)$ ; $\therefore P = \frac { 2 P _ { 1 } \left( T _ { 1 } T _ { 2 } \right) } { T _ { 1 } \left( T _ { 1 } + T _ { 2 } \right) } = \frac { 2 P _ { 1 } T _ { 2 } } { T _ { 1 } + T _ { 2 } }$