Q. 34

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 of the cooler side. Neglect the changes in the volume of mercury and of the glass.

Answer :

Let the curved surface area of tube A


Given


Length of mercury column=10cm=0.1m


Length of tube =100cm=1m


Pressure of mercury column P1=76cm of Hg=0.76m of Hg


Temperature of mercury column T1=27=300.15K


Temperature of air at cooler side T2=0=273.15K


Temperature of air at hotter side T’2=127=400.15K


Let the length of air column at cooler side be


The length of air column at hotter end be


Volume of cooler air =A


Volume of hotter air =A


Volume of mercury column = V


Pressure of cooler air =P2


Pressure of hotter air =P’2


We know that ideal gas equation


PV=nRT


Where V= volume of gas


R=gas constant =8.3JK-1mol-1


T=temperature


n=number of moles of gas


P=pressure of gas.


Applying ideal gas equation between cooler air and mercury column




Applying ideal gas equation between hotter air and mercury column




Under equilibrium condition the pressure P2 and P’2 will be same




Now length of entire tube


x+y+0.1=1


y=0.9-x


Substituting the value of y in equation (i)




(0.9-x)273.15=400.15x



So, the length of air column on the cooler side is 0.365m=36.5cm.


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