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A Glass Tube, Sealed at Both Ends, is 100 Cm Long. It Lies Horizontally with the Middle 10 Cm Containing Mercury. the Two Ends of the Tube Contain Air at 27°C and at a Pressure 76 Cm of Mercury. - Physics


A glass tube, sealed at both ends, is 100 cm long. It lies horizontally with the middle 10 cm containing mercury. The two ends of the tube contain air at 27°C and at a pressure 76 cm of mercury. The air column on one side is maintained at 0°C and the other side is maintained at 127°C. Calculate the length of the air column on the cooler side. Neglect the changes in the volume of mercury and of the glass.

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Let  CSA of the tube be A.

on the colder side : 

P1 = 0.76 m Hg

T1 = 300K

V1 = V

T2 = 273K

V2 = Ax  

`(P_1V)/T_1` = `(P_2Ax)/(T_2)`

⇒ `P_2= (P_1 VT_2)/(T_1Ax)`

on the hotter side : 

P1= 0.76 m Hg

T1 = 300K 

V1' = V
T2' = 400K

V2' = Ay

`(P_1'V)/T_1 = (P_2'Ay)/(T_2')`

⇒ `P_2' = (P_1VT_2')/(T_1Ay)`

In equilibrium , the pressures on both side will balance each other .

⇒ P2' = P2

⇒ `(P_1VT_2')/(T_1Ay) =( P_1VT_2)/(T_1Ax)`

⇒ `(T_2')/y = T_2/x`

From the length of the tube , we get 

x + y + 0.1=1

⇒ y = 0.9-x

`400/((0.9-x)) = 273/x` 

⇒ x = 0.365 m

⇒ x = 36.5 cm

Concept: Kinetic Theory of Gases- Assumptions
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 34 | Page 35
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