# a mercury thrmometer is not calibrated properly,but the intervals are equal in size.it reads 10 degree c when the actual temp is 25 degree c and it reads 65 degree c when the actual temp is 50 degree c.find the upper fixed point..pls show all the steps with explanation..any help would be greatly appreciated

Aman Bansal
592 Points
10 years ago

Dear Megan,

Thermometer design is a relatively simple matter. We measure the thermal expansion of a volume V of liquid by its expansion into a capillary of cross-sectional area A. Since the coefficient of cubical expansion is β = (1/V)(dV/dT), and dV = Adx, where x is the length of liquid in the capillary, the sensitivity of the thermometer, dx/dT = β(V/A). For β, we use the difference of the cubical expansion coefficients of the liquid and glass. Thermometers are not affected by vapor pressure above the capillary column, as a barometer would be. It is only necessary that the liquid be clearly distinguishable from the volume above the liquid. The glass capillary magnifies the column, and can be shaped to increase the magnification.

Mercury has β = 0.181 x 10-3 per °C, while ordinary soda-lime glass has β = 0.0276 x 10-3 per °C. The β of most liquids is on the order of 10-3, while that of most solids is about 10-5, so the solid expansion is only about 1% of that of the liquid. For mercury, the difference is β = 0.153 x 10-3 per °C. Suppose our thermometer has V = 250 mm3, with a capillary bore of 0.2 mm. The sensitivity will be dx/dT = 1.22 mm/°C, so a scale reading from -10°C to 110°C will be 158 mm long. This is actually fairly typical of small mercury thermometers. Mercury melts at -38.87°C, and boils at 356.7°C, so it is useful over a wide range. A mercury column is also very easily seen.

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Thanks

Aman Bansal