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?

Options

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

Answer

C

Explanation

`(P_(1))/(T_(1))+(P_(1))/(T_(1))=(P)/(T_(1))+(P)/(T_(2))`
`(2P_(1))/(T_(1))=P((T_(1)+T_(2))/(T_(1T_(2)))), `
`:. P=(2P_(1)(T_(1)T_(2)))/(T_(1)(T_(1)+T_(2)))=(2P_(1)T_(2))/(T_(1)+T_(2))`