# Mercury In a J tube

This is a doubt on question 5.3 from the 5th chapter of the book Heat and Thermodynamics by Zemansky and Dittman. The problem statement is as follows:

Mercury is poured into the open end of a j-shaped tube, closed at the short end, trapping air in that end. How much mercury can be poured in before it overflows? The length of the tube is given as 1.5 meters, effects due to curvature of the bottom can be neglected, and 1 atm = 76 cm Hg.

I get that at some point after pouring in mercury, the pressure of air trapped inside is so much that you can't further add mercury, thus leading to spilling. I also tried equating the product of the initial pressure and volume to the final pressure and volume of the air column. I took $$P_i=76 cm Hg$$ and $$V_i=(150cm)(Area)$$ and equated it to the final product(assuming isothermal conditions hold), taking the length of the air column as x cm, and final pressure as the sum of atmospheric and the pressure due to mercury column corresponding to the same horizontal level as the air column inside. But, the answer I am getting is 60 cm, which cannot be true as the shorter arm is given to be only 50 cm in length, and the air is trapped in the short end.

Could someone explain where am I wrong?

Edit: I am attaching a diagram as well. Here, x is the length of the air column and the shaded region is mercury filled in the tube. Initially, this tube was empty, open to atmosphere. • Please post or link a picture so that we can see dimensions. For one thing, this answer could depend on how much air is trapped. I really would need to see a picture. Mar 1 at 3:39
• No diagrams have been given in the text, but I will edit the post with a diagram I made. Mar 1 at 4:31
• As it stands, you drop this surprise with the last sentence that the short end is 50 cm, so clearly geometry was given. Mar 1 at 4:43
• I should have mentioned that the longer arm is 1 m and the short one is 0.5 m at the beginning itself, my bad. But yeah, no diagrams were given in the book, Mar 1 at 4:51