Saved Bookmarks
| 1. |
The area of cross-section of the capillary tube of a mercury thermometer is A_(0) and the volume of the bulb filled with mercury is V_(0) " at " 0^(@)C. Find the length of the mercury column in the capillary tube as the bulb is heated to t^(@)C. Coefficient of linear expansion of glass is alpha and coefficient of volume expansion of mercury is beta. |
|
Answer» Solution :Let `V_(g) " and " V_(m)` be the volumes of the bulb and mercury at `t^(@)C.` `therefore "" V_(g)=V_(0)(1+gamma_(g)t)=V_(0)(1+3alphat)` and `"" V_(m)=V_(0)(1+betat)` Hence, volume of mercury entering the tube is `"" V_(m)-V_(g)=V_(0)(1+betat)-V_(0)(1+3alphat)=V_(0)t(beta-3alpha)` If the area ofcross-section of the capillary tube at `t^(@)C " is " A_(t), " then " A_(t)=A_(0)(1+2alphat)`. If the length of mercury column in the tube is l, then `A_(t) times l=V_(0)t(beta-3alpha)` `therefore "" l=(V_(0)t(beta-3alpha))/(A_(0)(1+2alpha_t))"...(1)"` `""=(V_(0)t(beta-3alpha)(1+2alphat)^(-1))/(A_(0))=V_(0)/A_(0)t(beta-3alpha)(1-2alphat)` `""=V_(0)/A_(0)(beta-3alpha)t "...(2)"` `""` [neglecting `alphabeta " and " alpha^(2)` as they are very SMALL] Both the EQUATIONS (1) and (2), indicate the length of mercury column in the capillary tube at `t^(@)C.` |
|