Question

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

Answer: (D)

8.49 cm

Initially:

$l=45cm$ $(2l+10=100cm)$
$P_1=P_2=P\left(say\right)$ .......... (1)

Applying gas law at end A,
$\frac{45AP}{300}=\frac{(45-x)A{P}_1}{273}$ ........... (2)

Here, $A$ is the area of the cross-section.

Now, at end B, $\frac{45AP}{300}=\frac{(45+x)A{P}_2}{400}$ ......... (3)

From (1), (2) and (3):
$\frac{(45-x)}{273}=\frac{45+x}{400}$

$\Rightarrow x=8.49cm$