A uniform gets tube closed at both ends, encloses air columns of equal lengths 5cm,when the tube is placed horizontally.The pressure of the enclosed air is p.When the tube is placed at 60^@ to the vertical the upper and the lower columns of air are of lengths 46 cm and 44.5 cm respectively.Find the value of p.temperature of the system remains constant at 30^@C.

A uniform gets tube closed at both ends, encloses air columns of equal

1.	A uniform gets tube closed at both ends, encloses air columns of equal lengths 5cm,when the tube is placed horizontally.The pressure of the enclosed air is p.When the tube is placed at 60^@ to the vertical the upper and the lower columns of air are of lengths 46 cm and 44.5 cm respectively.Find the value of p.temperature of the system remains constant at 30^@C.
Answer» SOLUTION :Let the first case length of air column on each side of the mercury thread=l[Fig.6.11] Again length of the tube =44.5+46+5=95.5 cm `thereforel=(95.5-5)/2=45.25cm` In the secon case `p_2=p_1+5cos60^@=p_1+5/2` `=(p_1+2.5)cmHg` If in this case, `V_1` and `V_2` are the volume of the upper and the lower air columns in the tube, then according to Boyle.s LAW, `p_1V_1=p_2V_2` or, `p_1=46a.=(p_1+2.5) TIMES 44.5a` [where a=cross sectional area of the tube] Solving we GET `p_1=74.17 cm` Again, `pV=p_1V_1` or, `p=(p_1V_1)/V=(74.17 times46a)/(45.25a)=75.4cm` i.e.,`p=75.4cmHg`