Question

A glass capillary tube sealed at both ends is 90 cm long. It lies horizontally with a massless, thermally insulated pistion in the middle of neglegible thickness. The two ends of the tube which are equal in length contain air at ${27}^{\circ }C$ and pressure of 1 atm. The air column at one end is maintained at 300 K and the other end is maintained at 375 K. (Neglect the change in volume of the glass ) What is the pressure now in cm of Hg?

Answer 1

Assuming the sealed tube has a uniform cross sectional area then the volume willl be proportional to length. The number of moles of gases will be conserved on both side the sides.
$\frac{\mathrm{PV}}{T}$= constant
$\frac{P\times l}{300}=\frac{P\times l^{\prime }}{375}$
l' = 1.25 l
also l + l' = 90
l = 40 and l' = 50 now
$\frac{1\times 45}{300}=\frac{P\times 40}{300}$
P = 45/40 atm
= 9/8 *76 cm Hg
=85.5 cm Hg