Question

A glass tube sealed at both ends is 1m long. It lies horizontally with the middle 10 cm containing Hg. The two ends of the tube equal in length contain air at 27${}^0$C and pressure 76 cm of Hg. The temperature at one end is kept 0${}^0$C and at the other end it is 127${}^0$C Neglect the change in length of Hg column. Then the change in length on two sides is

• A. 12.3 cm
• B. 10.311 cm
• C. 9.9 cm
• D. 8.49 cm

Answer 1

The correct option is D 8.49 cm

Let the final pressure in the ends be $P$.

Since $PV/T=constant$ holds for both ends,

$\frac{\left(76\right)\left(45\right)}{300}=\frac{\left(P\right)(45-x)}{273}$

And $\frac{\left(76\right)\left(45\right)}{300}=\frac{P(45+x)}{400}$

Solving these two equations gives,

$x=8.49cm$